Well, I'll throw out the same disclaimer: somebody that's had guitar students is more likely to have useful input compared to me. However, try a couple of different picks. I use the black Dunlop Jazz III picks, and like Cliff said, they've got some picks with extra good grip. Looking at it from a physical point of view, maybe do some process of elimination. Like play something with only downstrokes and see if it happens, play something with only upstrokes and see if it happens, tremolo a single string and see if happens, because maybe it's related to a motion like the upstroke.