I have this problem sometimes, what you need to do, if you have the same problem as I do, it look at the male connector on the carrier, and the female connection on the tail light. Understand the mechanics of how the pieces connect. The snap piece on the carrier needs to be pushed out (towards the fender) sometimes in order to get it to stay. ALSO, make sure nothing is blocking the carrier from seating correctly on the tail light. Try to work the carrier on from side to side, not just directly snapped on front to back, but be careful of the bulbs.
Take your time, you should be able to figure it out, if not, you might have bad parts.