I have the following issue on two separate lowers and uppers and have no idea why it happens, so far only know how to fix it.

Rifle 1

M&P 15 lower - palmetto upper .223
Shooting Remington ammo

Rifle 2

M&P 15 lower - Sanders Armory .300 whisper
Shooting Remington ammo

Guns fire 2,5,10,15 rounds and then the trigger will not pull.  I am able to pull the charging handle and a new round in cycled but no trigger movement.  Sometimes the upper will not separate from the lower until I loosen the castle nut and turn the buffer tube 1/2 of a rotation.  When the upper is separated from the lower the trigger works fine.   I pull the trigger and the hammer moves forward, I don't let the hammer slam.  I put it back together and the issue is still there.  

Both use mil-spec triggers from the lower parts kit and the buffer tubes are from the kit.  I have not do any modifications on these rifles.  

Where should I look to start?  I would love to have a reliable AR-15s to shoot.  

Thank you.

Presuming you've checked the lower for debris (popped primer can really mess up the works), then my guess is that the disconnector is not releasing the hammer, either from incorrect assembly of the disconnector spring or excess overlap.

Pics or a disassembly video taken after it's bound up would help a lot in further diagnosis.

Lower won't separate until you loosen the buffer tube?  It's possible your buffer/bolt is getting stuck in the tube. An out of spec tube or one with a dent in it will cause this.  Learned this lesson the hard way, and is why my truck gun has a fixed stock now

Do both guns have the same buffer tube and buffer that you bought at the same time?  What brand are the parts?

What type and brand of buttstocks did you install on each gun?

Do both guns have the same LPKs that you bought at the same time?  What brand are they?

My rule is, 'Always listen to what the gun is telling you and don't try to force it to do anything.' I think your AR is telling you it cannot go into battery, which is also why the upper will not open - the bolt carrier is not clear of the receiver ring. Please do not try to fire it again until you have fixed it or had it fixed - you do not want it to fire out of battery, I can assure you of that. Problems like this are somewhat of a disadvantage with the Stoner design when compared to earlier rifles and the M1 Carbine with the bolt in full view and a handle to open and close it.
Open the upper and work the bolt carrier to see that it does or does not properly lock the bolt. Assuming it does (it should snap into battery easily, almost fall into lock if you tilt the upper), put it back together and manually cycle it (pull the charging handle back and let it snap forward) - it should go into battery every time. Of course the rifle should be free of ammunition, so you can snap the trigger after every cycle. Once it does all this, or fails to, you should have more of an idea what's happening.