I presenhtly have a couple of suction cup mirrors and the also kept falling off.

After giving the problem some thought i realised that the problem lay in the fact that when you use saliva on the cup it's not sufficiently viscous to keep it stuck on the windscreen so an alternative medium was required.
Now you may not like what I'm going to suggest but it does sort the problem very well.

Go into the garden at night in the dark and find a slug, the bigger and jucier the better

. Then you pick it up and turn it over sprinkle just a couple of grains of salt on the bottom bit that it slides along on.

It's very important that you use only a couple of grains of salt because if you use too much the slug will just turn inot a frothy slimy mess. So just a couple of grains of salt and the slug will exude tons of highly viscous colourless slime.

Use your finger tip to wipe this off the slug and smear it on the mirror suction cup, and then stick the mirror where you want on the windscreen.

It will dry in position and is guaranteed not to fall off ever again unless you decide to remove it in which case the slug residue is easily disolved away with a wet cloth.

It's just a case of finding the right medium for the task.