It happens sometimes and even in worse case than this one, when a duplicate is hinted at which is not applicable to the new question's setting or even solves a completely different problem.
What's the strategy you can adopt in this case?
First and foremost, when a vote for closing as duplicate is issued, a comment by the user who voted first is automatically added and you can reply to the comment, so that user can retract their vote.
However, as far as I know, that comment is removed when the question is actually closed, either by getting five votes or with the golden hammer. I'm not sure that comments addressed to one of the voters are notified to them, but that's certainly something you can try.
You can also edit the question explaining why the suggested duplicate isn't really good to solve the problem. The question will be bumped up in the front page and somebody may notice that the title has something like “not a duplicate” in it and investigate.
Maybe the duplicate is actually good and all it takes is some small change that can be added in comments (or in an answer to the duplicate) and in this case all is well. The title can be changed back or the question can be removed.
If after investigation it turns out that the question is not a duplicate, it will quite certainly be reopened. Wasn't it the case with yours?