good question. I am moving to a new state so I will be switching doctors so it is relevant to me as well. I would assume that you could simply ask your old doctor to fax all of your information to your new doctor, or just keep the original letter to give to any new doctor.
it would be pretty silly to have to keep getting letters every time you need a new doctor, like wise I think its silly that I have ot get a letter for top surgery when I am already on T for a year and living full time, but that's another story.