It sounds like the metal spring clip isn't actually snapping into place on the bumper cover. After I yanked out the sidemarker the first time, I actually looked in the owner's manual and saw the proper procedure for doing it, where you stick a screwdriver through a hole in the wheel well and pop the spring clip off the bumper cover.
If you just yanked it out and the spring clip bent back, there's a small possibility that you tore the part of the bumper that the spring clip is supposed to seat against. I hope that's not what happened in your case!
FIrst suggestion would be to make sure you're pushing the sidemarker all the way in so that the clip engages. If you're able to easily pull the whole unit back off, it's not working.