The mirror may just be sticking to the foam bumper at the top of the mirror box.
The foam gets gooey with age. It is quite easy to replace with similar thickness foam from a craft store. Or you can find foam light seal kits on eBay and such that will probably include the mirror bumper. If the foam has deteriorated it is probably safe to assume the foam seals etc in the rest of the camera are in a similar condition and need to be replaced.