I broke a few on mine as well when I removed them for re-paint & fixing eyebrows on the front. Luckily the front fascia only has a few studs mounted that way. On the rear, the ones most susceptible to shearing are ones along the bottom due to heat, moisture, & road dirt. I had to glue a few of those back in & I believe I used JB Weld which still seems to be holding. However, as Nick already replied I would use polyurethane windshield adhesive if I had to do it again.
The front spoiler is where I had the most broken studs, but luckily with that you can drill through & use nuts/bolts since those fasteners are not visible from the outside of the car.
Don't worry, the fascias are actually very repairable.
I struggled with this same problem many years ago. The frustrating part is that it is difficult to find an epoxy that will bond well enough to the urethane fascia. The act of installing the rear fascia usually requires some rough handling while pulling and popping the threaded studs through sheet metal brackets. Overtightening the nuts will often pull the studs loose where they've been glued with a weak adhesive. Lastly, the rear fascia, being made of urethane, has a lot of flexibility, and moves with changes in temperature - these things ask a lot from your adhesive.
Purchase the stainless replacement bolt plates. After you've ground out the old stud, clean the area very well with acetone, and apply GFlex epoxy according to the instructions. I am convinced there is no better epoxy for your purpose. It is not cheap, but it works well on plastics, as well as gluing dissimilar materials together. You can get it online, or at any West Marine retail store.
You can read more about it here: