It depends on the language of the policy. The language of the policy should be construed against your insurance company and in your favor. I would not be surprised if they simply don't want to pay. You should send them a letter saying you will consult with an attorney and asking for the exact clause in the policy they have relied in order to deny your coverage. That they paid for it in the past and now change their mind does work in your favor.
Law is state-specific and laws may vary from state to state. You should consult an attorney in your state for specific legal advice. This answer does not establish an attorney-client relationship.
The answer to your question is "maybe." First, it depends upon what type of coverage you have and whether it is covered by a federal law called ERISA. Secondly, it depends upon why they are claiming it is not appropriate or medically necessary. There are other issues, but those are the big ones.
I had a case exactly like that when I was still practicing Medicine, and after two weeks of denying my patient when I approached them as a physician, they only came around and covered her when I used some "magic words" as an attorney. In many cases, however, they can be made to see the light if a good health care attorney understands what to say and how to say it.
If you'd like to talk about it, give me a call and I'll be able to give you more information and let you know what would be involved in trying to "change their minds."