uww, you'll get told off for bumping your own posts haha.
Not experienced this on a 159 but have solved this and similar issues on the 156s I've owned.
If you have a look under the base plate of the mirror and see if there are any screws attached. On the 156 I think there are 3 which hold the plastic outer casing to the mirror base plate. chances are you're looking for something similar and just need to see about tightening these screws. The glass itself mounts to a mechanism which pivots off the mounting plate, so unless you manage to unscrew that the mirror shouldn't fall off.
if it gets really bad you may have to strip it down further, so you will need to remove the plastic triangle at the front of the door that covers the mounting point, this should just gentle clip off, although if they're anything like the 156 they'll be delicate so be careful. Behind that you should find 3 or so nuts that hold the mirror assembly to the car plus the electrical connectors, although they can be pushed down into door card sometimes so may need some long nosed pliers to pull them up.