Downrange,
Be very careful. If a cartridge provides the energy to only partially cycle the bolt, it may not have provided enough energy to push the projectile completely out of the barrel (squib), and you'll have an obstructed barrel.
A properly loaded cartridge provides enough energy for a full firing cycle: fire round, extract case from chamber, eject case, reset trigger, chamber new round.
My sincere advice is that the next time this happens to you, stop shooting, safe the rifle, and inspect the barrel for any obstructions.
A squib can be the genesis of a catastrophic failure.
S&W M&P 15 Sport Rifle Catastrophic Failure (exploding) - YouTube
In this video, the squib load had enough energy to extract & eject the case but not reset the trigger. You can see the WTH pause when the shooter pulls a dead trigger. He then manually charges the rifle, ejecting a live round, and chambering a fresh live round.
An AR-15 trigger will reset while the shooter is still pressing back the trigger. Separate your upper & lower. Cock the hammer & put your thumb on the hammer to arrest it's forward momentum so that it doesn't smack on the lower receiver. Press the trigger and let the hammer safely move forward. Keeping the trigger depressed, cock the hammer.
When you let off the trigger it should reset, and the hammer stays cocked.