Hi,
I am familar with A-T, but this would be a new one to be directly from A-T as far as I know. The main causes are likely Carpal Tunnel Syndrome, neuropathy (do you have numbness and tingling with reflex losses in your hands and feet?), otherwise a neck problem at the C6 joint:
Carpal Tunnel Syndrome is very common:
http://www.ninds.nih.gov/disorders/carpal_tunnel/detail_carpal_tunnel.htm
Note, A-T can cause neuropathy, both directly, and through Diabetes, so get that checked too.
Neck problems at C6 joint affects thumbs:
http://warwickphysio.com/uploads/images/images/Upper%20limb%20dermatome.jpg
A-T can cause Cervical Dystonia, which could affect the C6 neck joint. Do you have any problems with muscle stiffness/spasms in the neck? See here for symptoms:
http://www.dystonia.org.uk/index.php/professional-research/types-of-dystonia/cervical-dystonia
"ATM has previously been reported to cause isolated cervical dystonia, but never, to our knowledge, DRD [Dopa Responsive Dystonia]. Individuals with dystonia related to ataxia telangiectasia may benefit from a trial of levodopa."
http://www.ncbi.nlm.nih.gov/pubmed/23946315
So, if it's Carpal Tunnel Syndrome, it can be treated various ways, depending on cause. Get your blood sugar amd thyroid checked too. If it's a neck problem, ask your Neurologist to try you on Levodopa, the med usually used in Parkinson's, which may help, otherwise Botox injections in the affected muscle could help.
Do go and get this checked out, because it might be treatable, and that'd be at least one less issue you've got. :-)
Yours,
Abs