I do a bit of woodworking and whenever I use brass screws I dip the screws in beeswax before screwing them in the pre-drilled holes because they often snap in harder woods because of hard friction.
I don't know if this is the problem you've had but some plastics can have a similar friction, enough to snap screws.
A little dab of wax, or some other kind of lubricant, is never a bad idea!
Small screws are often much harder than large ones because they're hardened through whereas larger ones have a softer core and doesn't snap as easily, that's also part of the problem I guess...
I hope the third time is successful but add some lubricant just to be sure