Didn't stick to what...?....old black plastic mirror cover?
If "Yes", then as Hooligan said, degrease the black plastic that been exposed to the elements (or like mine, treated with VRT to look new); get your self a new roll of 3M adhesive tape, and replace the old tape on the mirror cover...
Plus one more essential step for good adhesion.."adhesion promoter", by pad or pen. I buy the adhesion promoter "pen".....it goes a long way on many jobs, and not much more expensive than a couple of rip-open pads.
Here's one site. But, you can Goggle for it and get it as cheap as you'd like!
Adhesion Promoter Pen - Dash Care Products Automotive Adhesion Promoter Pen 4298
Personally, I have done custom painting on the covers for
soonercruiser. So, I put on just enough to still make it occassionally removable enough to touch up the paint.