I apologize for the newbish post. I've talked with a few friends and relatives that have built plenty of AR-15s, yet they have never come across the problem of the hammer becoming stuck and not fully resetting to the fire position every so often, not every time. The quick safe solution to solving this at the range I found was to ever so slightly switch the safety from fire to safe (not completely switching to safe) then the hammer would pop back up to the correct set position and would be able to continue firing. I know it's not such a problem flip the safety, but I figured being my first rifle build I would like it to function smoothly. This video shows how mine gets stuck (not my build or video), but I would love some input on how to fix it. My hammer does not lock as tightly like the one in the video, a simple tap or two of the trigger would reset it correctly. Thank you for any help!

The video. Someone much smarter than I will come along and tell you exactly what's wrong but in the mean time are the springs installed correctly?

I appreciate the help with the video. I have had a couple of people look over the rifle, and they made sure the build was assembled correctly before I fired it. The problem revealed it's self with firing it. Since identifying I had someone that has built a half dozen and they found the issue weird how sensitive and easy it was to reset. Unlike the video, as I added, the safety movement or simply tap of the trigger would reset it.

What kind of trigger?  Just a reg. mil-spec?  I guess the hook on the hammer or disco could be out of spec.  Just for shits and giggles I'd pull out the trigger and safety and then reinstall.  But you could just wait and see if anyone else has any ideas.

Had the same problem with a rifle my son built... replaced the trigger group and problem fixed.

The hammer and disconnector did not play well together, one or both were out of spec.

When you swing the hammer back manually (without pulling the trigger) does the hammer sear touch the disconnector sear as it passes by? Ideally, the hammer and disconnector sear should not actually touch. You want about the width of a hair between the sears.
If the hammer and disconnector sears are to close, it can sometimes cause the hammer to hang up on the disconnector. Sometimes the hammer or disconnector sear surfaces can be rough or have a ridge that causes them to hang up. Sometimes the angle of the sears is off enough to hang up.
Make sure the hammer spring and disco spring are installed correctly. If everything is installed correctly you could replace the hammer or disconnector or both to try to resolve the problem.
You could also examine the sear surfaces to determine why they hang up and polish or reshape them. Since touching the trigger allows the hammer to release from the disco, it's not binding much. Polishing out an imperfection may be all that's needed?

I had the same problem OP. I lightly sanded and polished the areas of the upper two red circles and that fixed it.

I had the same issue with a recent build and traced it to the selector switch being slightly out of spec. Rather than deal with returning it for a replacement, I use a file to remove the offending material and it works perfectly, now. Look to insure the trigger base is not hitting the sides of the notch in the selector switch.

I've noticed that with cheap LPK's that I've picked up recently (namely combat Armory and from ar15discounts.com). I ended up just buying a new disconnector after taking too much off the one it came with. I've now vowed to just spend an extra $10-20 to get a higher quality LPK when I need one, or at least buy a new disconnector.

OP -  where did your LPK come from?