Can a procedure be

There are situations where they could refuse to cover it now, such as:
1) Your insurance lapsed before the actual surgery--they only have to cover if your insurance is still in place when the procedure is performed.
2) Something changed between when they approved it and when you had the surgery--for example, it ended up being done by a surgeon or facility which was not part of their network; the scope or type of surgery changed from what you told them it would be, and what was done is not covered. An approval is only good for the facts on which it was based.
3) They discovered some fraud or misrepresentation (basically lie) in what you had told them in order to get the procedure approved--a misrepresentation lets them disclaim or avoid coverage.
On the other hand, if everything you told them to get the approval was accurate, nothing changed since then, and your insurance is still in place, they should be covering the procedure and honoring what they told you--if they won't, you could sue them for breach of contract (an insurance policy is a contract), for violation of the implied covenant of good faith and fair dealing (the obligation to essentially not cheat or abuse the other party to a contrract), and/or on promissory estoppel (you made significant plans--surgery--based on their promises that it would be covered, which promise it was reasonable for you to rely upon, and so they should be held to it; promissory estoppel cases are difficult, since the law does not like enforcing promises which are not themselves part of or made in a contract, but it is another possible ground to hold them to what they said which you could bring up).