I have an Aero Precision M5 build that is sometimes not ejecting.  The spent casing will extract from the chamber but just sit on top of the next cartridge causing a jam.  If it's the last round the bolt will lock back and the spent casing will sit on the empty magazine.  The upper and lower were complete from Aero and I used a Ballistic Advantage 16" midlength stainless barrel with gas block pinned by BA.  The buffer tube is carbine length but I can't find a marking for the buffer weight but seems pretty tight when using the charging handle to chamber a round.  I was shooting the rifle suppressed with an AAC can.
I was using factory Hornady 168 grain TAP ammo.

You said that the last round holds the bolt back so I will assume that you  are not under gassed. When the casings do eject, what position do they eject?
Of the short list, it is possible that you're over gassed
What do the casing heads look like from the extractor?

My guess is it's over gassed. AR10 are notorious for being over gassed, especially with a can. Usually an adjustable gas block fixes it right u.

Did you clean and lube the bolt and extractor? Some bolts also have problems in the gas ring area so just to be sure make sure the gaps in the rings are not aligned. Check your magazine, take it apart, clean it, dry lube the inside and if you can, replace the follower with an anti-tip style. While it may be that none of these things are the culprit it will at least eliminate them from the equation and narrow your focus while trying to correct the issue.

It's really difficult to over or under gas a .308 without altering the gas port in the barrel, they pretty much just run. However, a misaligned gas block may provide enough gas to just barely lock on and empty mag and still be under gassed for reliable operation. For example, when I set up an adjustable GB on a .308, I fire single rounds and adjust the gas block until the bolt locks open on the empty mag. I then open it one full turn further to provide reliability. The last question I have is did you install a .308 buffer and spring? The buffer tube length can be either a rifle or carbine length provide the correct spring and buffer are used. A .308 typically seems to run well with an H2 buffer since it needs a more prominent dead blow effect to strip the round and go into full battery.

Thanks for the replies guys.

I'm new to the .308 AR platform and it's a brand new build.  I ran 20 rounds through it as a break in, via BA's guidelines (un-suppressed)  and about 35 rounds yesterday all suppressed.  I did have the same problem suppressed and non suppressed.

I'm using 168 grain A-Max TAP Precison

10 round P-mags

Ejector seems to be fine, but is extremely hard to get back together.  Spring seems very stiff

My gas block is not adjustable, and seems straight, it was installed by Ballistic Advantage

I cannot remember what the casings looked like.  They were super dirty due to the suppressor

The rounds that did eject were at about 3-4 o'clock

And finally, The buffer spring and weight came with the lower which was a complete lower from AERO.  There are no marking's on it, but would guess it's what Areo would recommend.  I have no idea of spring or buffer weight though.

Hope this helps narrowing down my issue.

It's beginning to sound more like a break in problem. Load your mag up and let it sit for a week, that will break that in. I'd probably run a 100 rounds through it un-suppressed just to let the BCG find it's home and give the bolt a work out. Run it wet and see if the problem clears up.

I’ve got a similar rifle from aero. Was having some similar ejection problems and the cases were getting dented really bad. Switched to a  adjustable gas block, Dialed the gas down and it’s much better. Recoil is also noticeably less felt

OP, any gouges in the rear of the magazine follower?

Thanks for all the replies.  No gouges on the magazine follower.  I did contact Aero and BA.  Aero stated their NiB BCG's come assembled with 2 O-rings on the extractor.  They recommended removing one of the O-rings and seeing if that helps.  I'm going to give that a try and if that doesn't work, I'll go with an adjustable gas block.