Short stroking  (Failure to cycle)
Short stroking on an AR rifle is when the bolt carrier group does not cycle far enough to the rear to be able to strip a round from the magazine and chamber the next round.  After firing a round, you will notice that the bolt is closed on an empty chamber, forcing you to manually cycle the rifle to feed the next round.  This occurs when there is an issue with the gas system.
To see if you have a short stroking problem and not a “Failure to Feed” problem please perform this test first.  (assuming your bolt catch and magazine is functioning properly)   Insert one round into a magazine that you know to be performing well.  Insert the magazine into the magazine well, pull the charging handle to the rear, release the charging and load the round into the chamber.  Safely discharge that round.  After the round has been fired the bolt should automatically be locked to the rear.  If the bolt is closed on the empty chamber, then it did not travel far enough to the rear to be held by the bolt catch, and your rifle has short stroked.
Short stroking is a symptom of a problem of the gas system in the rifle.  There are 7 parts of the AR gas system.  In the upper receiver group, you have the barrel (gas port), front sight base, and gas tube.  In the bolt carrier group you have the gas key, the carrier, the bolt, and the gas rings.

Assuming the rifle was running correctly previously (in the exact configuration it is currently) The following is a basic trouble-shooting checklist.
1)  Ammo issue ?  Commercial ammo does not run as hot as Milspec ammo, and some lots of commercial ammo may not be strong enough to cycle the weapon.  Try a completely different type of ammo.  If the weapon works correctly then you may have some bad ammo.  This is becoming a more common problem with some of the low cost imported ammo, especially with milspec sized gas ports.
2)  Lube and clean the rifle.  Pull out your GI manual and properly clean the weapon.  As a note, a little bit of dirt and carbon should not stop the proper cycling of your rifle.
3)  Check the carrier (gas) key.  If the carrier key is loose the gas system will not hold enough pressure to fully cycle the weapon.  Try a different carrier that you know to be working in another properly functioning weapon.  If the weapon runs well with the other carrier, you may have an issue with your carrier key.  The carrier key bolts should not be loose.  It should be staked from the factory.  Check to make sure the bolts securing the key did not rotate past the staking.  The bolts should be torqued to 35-40 in/lbs.
4)  Check the gas rings.  (or just go ahead and change them – they are very inexpensive)  Mythbuster:  The gaps in the gas rings do not need to be staggered.  I know we were all taught otherwise in recruit training, and yes I know it says they must be staggered in the GI manual.  But this is a myth.  As a note; it will not hurt the system to stagger the gaps in the rings, but if this single change makes the difference – you need new gas rings ASAP.  Inspect the rings, make sure there are 3 of them, and that they are installed properly.  Disassemble the carrier group, insert the bolt into the carrier, and hold the carrier vertically in the air.  The bolt should not fall out of the carrier.
5)  Change the gas tube.