I just remembered one other idea I meant to share. It's sometimes recommended in Dysautonomia that individuals prepare for a procedure with IV fluids. This is especially helpful for people with frequent fainting episodes.
The effect of anesthesia is really different for everyone, and can be dramatically different in individuals with Dysautonomia. I'd recommend insisting on a heart monitor, and possibly supplemental oxygen just to be sure. Also have the number to the closest hospital, and your specialist available to the dentist before the procedure.
After the procedure, you shouldn't be expected to leave unassisted. It's important to have someone with you that understands your condition. This person can bring you to the vehicle in a wheelchair.
Give your dentist as much information about your condition as possible. For example, the articles that Heiferly recommended. Good luck!
I have been under general anesthesia three times since having POTS. In my experience, it hasn't been any different than being under anesthesia before I had POTS except perhaps more fatigue (but it's impossible to separate the effect of the anesthesia, the reaction of the body to the surgery I had itself, and the side effects of the pain killers I took immediately after surgery). I had no adverse effects from anesthesia, other than that I always have to take anti-nausea medication afterward (as many people do).
That being said, everyone is different, and it may be a totally different experience for others. I would strongly recommend to your dentist that she read the medical journal articles that have been published putting forth guidelines on dental anesthesia and POTS if she has not done so already.
For example:
Brooks, John K., DDS and Francis, Laurie A. P., RDH. Postural Orthostatic Tachycardia Syndrome: Dental Treatment Considerations. J Am Dent Assoc 2006, Vol 137, No 4, 488-493.
http://jada.ada.org/cgi/content/full/137/4/488
Anesthesiology:
August 2000 - Volume 93 - Issue 2 - pp 571-573
Case Reports
Perioperative Considerations in a Patient with Orthostatic Intolerance Syndrome
Mchaourab, Ali M.D.; Mazzeo, Anthony J. M.D.; May, Judith A. M.D.; Pagel, Paul S. M.D., Ph.D.
http://journals.lww.com/anesthesiology/pages/articleviewer.aspx?year=2000&issue=08000&article=00041&type=fulltext