I can't think of anything that would cause what you are describing. The first thing I would suggest is plugging up to BF, power the quad with props off, and see if you can detect it on the bench in the Receiver tab, and maybe see if you have any Deadband set also.
A few questions to help me better understand...
How long after you take off does this "fall asleep"?
How long after you wiggle the sticks does it take to fall back asleep?
Once you give it a wiggle then it rolls left or right with full authority?
Is this with defaults in BF, and what rev are you running?
What quad do you have?
What TX and RX are you using?