The left hand side of the silver tailgate trim that sits above the registration plate has been coming loose on the left hand side and now I'm worried that the right hand side might be coming loose as well.

 

What is the best way to secure it? I'm not sure if something has snapped or just weakened, my guess is that whatever clips are used to hold it in place are either broken or no longer effective.

 

My mechanic tried to glue it - I'm not sure what type of glue he used - but the glue came off within a week.

I would be tempted to remove the cover from the inside of the tailgate and see if you can secure the trim from behind (maybe a self tapping screw would be sufficient to hold it)