Hi!
Invisalign should not cause any loose teeth, regardless of age. In fact, there is no age limit for orthodontic treatment. I currently have patients in their 70s in treatment with great results and no side effects.
There are 2 considerations with adults.
The first one is that they should have healthy supporting bone and gums. This is usually accomplished by undergoing an examination by a periodontist (gums and bone specialist) prior to orthodontic treatment.
The second is the careful planning of where teeth will be moved to, since even in people with healthy bone and gums, this can cause problems if not done correctly.
You should not have any problems if you see an orthodontist for your Invisalign treatment and they make sure your teeth, gums, and bones are all healthy before treatment is begun.
Hope it helps!