Sometimes questions are posted that are too vague or broad and they are simultaneously voted for closure and asked to provide more information. If the OP manages to edit the question before it gets closed (presumably to add the extra detail necessary as requested) the close vote count should be reset. This will give poorly worded questions that have been subsequently improved a fair chance at an answer without its history overtaking it.
There is no guarantee that editing the post made the post any bit better or more worthy of staying open.
If you are going to potentially reset the votes, you need to give those votes back to the users who already voted so that they can vote to close it again. But even then I am against this, because you can't expect every user who goes and votes to close to keep tabs on every item they voted for in case it gets edited.
If you post a duplicate or something that is clearly not belonging, editing it is not going to make a bit of difference, so all you are doing is canceling out the votes of those who already came by. Expecting them to come BACK to cast the same vote yet again is senseless.
I like the purpose behind the idea, but this idea would simply not accomplish it's purpose.
What it would effectively do is make it impossible for a contentious question to be closed. If a user (or users) are trying to keep it open, they could simply continually make little edits to it, and it would be completely unable to be closed. This would cause huge edit wars, and would completely nullify the purpose of the close vote in the first place. It would mean that only moderators have the ability to close questions.
I think that would give a too-easy getaway for people asking "bad" questions, so I'm against it.
Bottom line is I think the disadvantages of your suggestion outweigh the advantages, and I believe such a feature will be abused. It's not as if these scenarios don't currently have a solution - if the editing made the question "good", it will be reopened by the community.
If a question gets edited well enough, to the point where its gone from a question that was getting close votes, to a question that should be open, the same group of users who could have and perhaps were voting to close, can and likely will vote to reopen the question. Again, assuming the edit made the question worthy of being open. Automatically assuming an edit fixed the reasons people were voting to close, I think would be very unreliable.
There would need to be some kind of way to programatically determine a proper edit. This could very easily be abused, which would quickly invalidate your presumption of adding necessary info. I think it'd be better for the OP to edit the question and request it be reopened. They should be putting more thought into formulating proper questions (IMHO).