My mirror fell off - my dealership got it sorted through a windscreen company, who used special bonding stuff. Seems to work, hasn't come off since....
You can buy mirror pads at all good car parts places (halfords) about £1.00 each.
Make sure both surfaces are clean (white spirit) before applying.
If fitting on a cold day lightly warm up the areas to be bonded first.
I used tape on mine originally, but because the Abarth mirror is a right beast [rain sensors, light sensors, wires, trim around it, etc] all this did was push the trim away from the windscreen so it wasn't flush and rattled like anything....
Best stuff i ever used was from HellFrauds of all places.
Comes in a pack, little plastic mesh sheet and some glue, this bonds permanently to the screen. And i mean permanently, i then got a cracked screen and removing the mirror they took glass with it!