Is your gun failing to extract or eject, as they are different issues? Is it failing to extract where it is leaving the empty casing in the chamber, or failing to eject where the empty casing is being extracted from the chamber but the bolt carrier isn't going rearward enough to eject the empty casing?  

If it is failing to extract the empty casing (leaving the empty casing in the chamber), then how are you able to get the casing out of the chamber?  If you can manually cycle the action and remove the empty casing, then you may have a weak extractor tension, bad or dirty extractor, rifle that is unlocking too early, etc.  If you manually cycle the action to remove the non-extracted empty casing, and the extractor won't grab it, then is the lip ripped off the empty casing which indicates that you have strong extractor tension, but may have a rifle that is unlocking too early, over pressured issues or possibly soft brass cased ammunition, etc.  If you have to run a cleaning rod down the barrel to force the empty casing out, then you have to look for what is holding the casing in the chamber (dirty chamber, lube or fouling, rough chamber, etc).    

If the empty casing is being extracted from the chamber, but not being ejected, then you possibly have lack of gas pressure (gas leak, soft ammo, etc), something hindering the bolt carrier from traveling all the way rearward, rifle is cycling too slow, friction where the bolt carrier is dragging inside the upper, barrel nut is not aligned properly causing friction on the gas tube/carrier key relationship, lack of lubrication on the 7 bolt lugs & rails of the bolt carrier (Use a quality lubricant like Slip2000 "EWL" Extreme Weapons Lube), dirty or fouled chamber, etc.

CY6
Greg Sullivan "Sully"
SLR15 Rifles
TheDefensiveEdge.com
(763) 712-0123

From the pic, the empty casing appears to be partially extracted out of the chamber.  Can you manually cycle rounds through the rifle with no issues where the cartridges are extracted and ejected?  Any chance you post a pic of the bolt face showing the extractor, and also any chance of getting pics of the empty cartridges that are failing to extract showing possible markings or signs that might help to identify where the problem is at.  Does the extractor have an O-ring under it, if it does then remove it to see if there is a difference, if it doesn't then try using the O-ring and see if there is a difference?
 
CY6
Greg Sullivan "Sully"
SLR15 Rifles
TheDefensiveEdge.com
(763) 712-0123

Clean the chamber with a chamber brush and CLP by hand.  Once you have the chamber clean and dry, take a good look at the chamber.  It should be smooth as a mirror with not reamer chatter/ridge/grooving marks.

Solvents, you use what you want to clean the actual barrel bore to start with (would stay away from hoppes since it leaves a nastly residue behind), but the rest of the rifle gets cleaned and lubed with CLP.

When cleaning the B/C, make sure to pull the extractor to clean up it's bolt channel and the grabbing claw of the extractor.

With the rifle correctly cleaned and lubed, need you to load a single round in the mag, insert the mag, charge the round, and fire the round with the empty mag still in the well.  Did the bolt lock back on the catch, and is the catch in front of the bolt face?

Lastly, need a photo of a spent case to see how smooth the chamber is, and a photo of the extractor so I can see if claw section.  Hence want to check the bottom ends of the claw, and the side of the rim releif channel under it for edge burs that may need to be removed.   Also, do not clean the extractor before you post photo's, since I want to see the amount of brass scrapping flakes that the extractor and bolt channel have in them.

Hence want to make sure that you are using the correct solvents to clean and lube the rig to start with (so we can weed out a solvent problem choking the rifle out quickly to start with), what to make sure that the chamber is smooth and rifle full stroking to start with, and to make sure that the problem is not either the extractor having milling burs that need to be removed, or just the B/C getting packed with brass flakes to block the extractor partially open isntead.

Looking at the dents in the shoulder and mouth area of the casing in the pic above, this looks like the dents occurred when it was a live round that jammed under an empty casing that failed to fully extract (like in your previous photo above), then somehow that dented live round got into the chamber and fired.  IMHO when a live round gets a large dent, I would not recommend chambering and firing it, as it could cause issues of fail to extract from being too tight, or something like a catastrophic failure.

Is it possible that you are having a feeding issue, where rounds are getting damaged before they are chambered, and the dented casings are not wanting to extract?  If the live rounds are getting dented upon feeding, I would look at the magazines being used, possible tension on magazine catch being too tight or loose, or possible feed ramps.
     
CY6
Greg Sullivan "Sully"
SLR15 Rifles
TheDefensiveEdge.com
(763) 712-0123

Again, need a close up of your extractor, the bolt channel for it, and the conditions of your cleaned chamber to see if there is problems.

Hence such as in the below.

Again, need to the see the areas that I showed above in my post on your extractor, bolt, and chamber. Hence you can drop on a #60 O ring (about a dime at any hardware store) around the extractor spring to band aid the problem and that may work, but best to just solve the problem without have to band-aid in the first place isntead

Short of that, just box the rig up, and send it to BCM to check out isntead.

Quick check to see if someone is using a chamber brush with CLP by hand correctly to get the chamber clean (end of chamber cut as well), spin a new 30 cal mop with just a hint of CLP in the chamber with a drill and section of cleaning rod after they done/chamber is dry, and make sure that the mop is staying clean.


As for heaver buffer, if the gas port is way over sized, but most of the time the problem comes back to either not cleaning the chamber correctly, or the chamber is a mess with reamer chatter isntead (groove and ridging, and the chamber walls not mirror smooth isntead).

To add, if the chamber head space is too tight,the reloaded case not correctly trimmed, or reamed 223 and you are running 5.56 Nato through it,  it will cause short stroking problems.

Round count for the above photos since cleaned, and what are you using to lube the upper receiver bearing areas.  

With the looks of the chamber and the lube that has migrated to what should be a dry chamber, guessing some type axle grease/not CLP, and 100's of rounds since the last cleaning as well.

Step one, go buy a large spray can of BreakfreeCLP, and a chamber brush.




Shake the hell out of the can and light up the inside of the receiver, the chamber, and even give a good shot of CLP down the gas tube from inside the receiver and allow it to run out of the barrel gas port into the bore.

Now break out the chamber brush on a single section of cleaning rod, and use it to give the chamber and barrel extension void the scrubbing of it life.  Hence not only are you going to work the chamber brush in and out of the bore, but twist the chamber brush so it cleans the inside of the barrel extension void as well.   Give the chamber another shot of fresh CLP, and then start cleaning the upper receiver with paper towel, Q-tip (works great for inside the barrel extension void) and then run clean patches from the chamber to the muzzle until you have the chamber and the bore dry.

On the B/C, pull the bolt off, remove the extractor and light it up as well with CLP, give the parts a good scrubbing, then wipe off the fouled CLP from the parts.

On the lower receiver, remove the buffer and spring, give them a good shot of CLP as well as inside the tube, and clean all the fouled CLP from them.

Now on the buffer and recoil spring, light coat of fresh CLP, and them put them back in the receiver extension.

At this point, need to see a photo of the parts,

As for B/C, light coat of CLP inside and out when you are putting it back together, give the charging handle a light coat of CLP, then drop the charging handle in, drop the CLP wet B/C into the upper, lock the upper home and cycle the empty rifle action a few times to migrate the CLP off the B/C to the upper bearing areas.

Since we are using CLP as the lubing agent (as well the the cleaning agent) we need to be very careful with what out types of solvents we are using on the rifle a well.  Hence item like Hoppes are out, since they will leave behind a resudie that the cleaning agent in CLP will try to disolve, turning the two into a sticky mess isntead.  Bluntly, shot of the above, the only thing that I have left out is cleaning the actual bore of the rifle instead, and here we begin cleaning it with a good copper solvent like Sweets that does not require a lot of scrubbing to remove the copper fouling.



So once we are back from the range, we start with first cleaning the bore of the rifle with sweets and a brass brush, then use dry patches to push out the Blue fouling until the patches are coming out dry and clean.  Then we break out the CLP to clean the parts are noted above.  Hence Sweets leaved behind no residue, and when we clean the chamber and push out the fouled CLP next, there will be enough remnants of CLP in the chamber and bore for short term storage.



Ok, now lets say that the chamber and extractor check out, the gun has been correctly cleaned and lubed with the correct solvents, We need to feed test the rifle.
Pick a mag, load only a single round into the mag, insert it into the well, charge the round, and fire the single round with the empty mag still in the rifle.
Did the bolt lock back on the bolt catch????  Hence catch in front of the bolt face, and not under the carrier isntead.

If the bolt locked back on the cleaned and lubed rig, then all is good and time to do the live fire.  The standard practice to keep a AR from choking out, is about every 200 rounds, pull back on the charging handle until you see the gas ring move in front of the carrier side gas ports, and add a good shot of CLP into gas chamber section of the carrier.  The fresh CLP added here will migrate through the rifle as needed to allow the CLP to dissolve the power fouling to prevent the rifle from choking out.    If you do have problems and ran the rig too long and it starts to have problem, then pull the B/C out of the upper, give it a fresh coat of CLP inside and out (right over the fouled CLP on it), empty cycle the action a few times, and go back to shooting.
To add here, if you are going to shoot ammo that seams to burn less than clean, or coated steel case ammo, run the upper bearing surfaces on the wetter side with CLP.  CLP has a cleaning agent in it, and will help to combat the fouling problem and keep the ammo from fouling choking out instead.

Bottom line, the rifle does not look it was first correctly cleaned and lubed before being shot the first time, hence to remove the assembly grease/long term grease on the rig used to keep it from rusting as it sitting waiting to be sold, and may be most of the problem.

Note Again, I want to see photo's of your chamber to weed it out as a reamer chatter mess, the extractor to make sure it not a bur mess, and not sure If I asked this question, but if a gas block instead of a FSB on the barrel, make sure that the set screw are tight, and they where installed with Loctite.  I'm still suspect of this whole mess being a cleaning lubing problem (could be from a mix of Hoppes and CLP), but would like to weed out a gas block loose problem as well.