A picture of the brass that got stuck will tells us a lot. As it is, it could be any number of things.
Stuck/broken extractor. Spring missing from under extractor. Bad ejector or ejector spring. Gas system not fully cycling. Improper buffer or buffer spring installed causing a short stroke condition. Cracked gas tube.
Need more info.
Try an extra power spring for the extractor and/or an Oring over the same spring. Previous poster suggesting AR15.com is a good start, also search for fte and ftf with ar15s. My experience is the extractor is a good place to start.
I had a guy bring me an AR which he wanted to mount a piston kit to because his rounds were not cycling right. Turned out his gas tube was pinched by a loose barrel nut. If the barrell had roatated further (if the tube was not holding it from rotating off) he could have blown it up in his face!. I used a brand new barrel nut to reattach the barrel when mounting the piston kit.