I know the rear bumper/fender mounts can degrade and I suspect mine have but the price!
What noise do they make when loose?

 

If you can physically move your rear bumper. up and down, the mounts are on their way out. The brass inserts that the mounting bolts secure to have almost certainly parted company with the mounts.

All is not lost however. I managed to remove my bumper cover from the beam without destroying the mounts which unfortunately is the usual method. I was then able to unbolt the mounts and beam, resecure the inserts and refit the whole bumper. I would double check the state of the mounts before resorting to their destruction.

Briefly, my method was to gain access to the plastic fittings that secure the cover to the beam by pushing the bumper down and using a modelling blade to cut through the fittings. Once the fittings are severed you can remove the bumper cover. That then gives access to the mounting bolts.

I refitted the brass fittings into the mount using epoxy glue and a few self tapping screws. I drilled small holes along the edge of the brass fitting for the screws. I then reattached the bumper cover to the beam before refitting it. The fasteners are readily available in any auto store.

When refitting the bumper mounting bolts I used an anti sieze to help prevent a reoccurrence.
I'm sorry that I didn't take photos.

Hopefully you will find that your mounts are retrievable. Good luck

 

Thank you for that advice which I'll probably follow as the bumper does move.