How to keep Presta valve insert from detaching after inflation?
I've had this happen with some tubes - Continental, maybe? Conti tubes are compatible with valve extenders, so the valve on them does come off like this. You're probably screwing the chuck on too tightly, and then the valve comes off with it.  

Or maybe some tubes come with the valve not properly torqued.

And after it did come off, you probably didn't tighten the valve tight enough into the stem to stop it from happening again.  There should be small flats on the side of the valve portion that comes off - you need to use a wrench on that when you rescrew it into the stem.  Be sure to hold the stem with a pair of pliers when you do this to prevent the stem from twisting.  If you don't you can tear the tube.

Worst case, put Loctite on the valve threads if it keeps happening.