YUP - most mirror heads use a simple ball and friction plate. They wear. If you cant adjust for wear - well you're screwed.
Some have little screws that allow you to torque down the friction plate. ime - the fancier the mirror the less likely it is they allow "fixing".
There is anther "fix" but it can look ugly - I sit on the
Function over Form side of the fence so it's not a biggy for me.
Find something like REPAIR TAPE Or non vulcanised rubber and add support to the swivel. I don't know the details of the mirror - but sometimes a BIT FAT O-Ring works.
This resists vibration/movement - - But YOU can make it move. I've used this system on odd nuts where Nyloc etc is not available
Are these what you have?
http://www.triumphmotorcycles.co.uk...780A66F}&selectedBikeName=Rocket-III-Roadster