Notifying us of updates sounds alright; I'd be willing to be a guinea pig in an experiment of how that'd work out.
However... Absolutely do not remove our close votes!
A question being edited is not in itself reason enough to suspect it no longer warrants closure. (It certainly doesn't warrant removing all efforts to close it so far.) The issue here might be to ensure questions worth keeping open don't get closed, but we already have mechanisms in place to prevent that.
Bear in mind that close votes rely on a steady stream of people visiting the question, reading it, and voting to close it, and this process often takes a few hours, except during very active times. But the close process needs to be fast to avoid messy situations. Quoting C.Ross (emphasis added):
I don't have a great answer, but this is why it's important to quickly place questions in need of editing on hold. – C. Ross♦ Jun 27 '13 at 12:47
Let's assume a question receives three close votes, then gets edited. After that edit, there's it's either worth keeping open, or not (in the eyes of readers). New visitors will come along, and will either...
- think it's worth keeping open, and do nothing, or
- think it needs closing, and vote to close it.
If everyone new visiting the question thinks it's good enough, a Good Enough question is protected from closure simply by virtue of nobody else trying to close it. Otherwise, if enough people think it needs closing, it'll be closed.
If everyone who voted prior thinks it's actually good enough now, they can vote to reopen.
But if close votes get removed with edits, the process slows down.
Let's consider the scenarios again:
Scenario A: For a question that becomes good...
This is fantastic at protecting those questions from closure. They're good, the old close voters think so too, new visitors think so too, everything's fine and the question stays open.
Scenario B: For a question that remains needing closure...
If a question accumulates three close votes, then gets edited, then three new people vote to close, ordinarily it would already be closed by this point.
At this point, though, it isn't: it has to wait for a further two new visitors, or for the three people originally to come back. We are not universally available people; that might be a few hours. Then the asker might edit again.
Each edit stretches the closing process out longer, but the question still needs closure. Remember, this is a scenario where the question still needs closure: at any point it can revert to scenario A, but for now we're sticking with Scenario B. Maybe it's an inherently opinion-based question, and no amount of editing will save it.
Furthermore, speaking for myself: I'd find it frustrating to have to revisit the question, and voting to close something for the second or third time that still needs closure. This is much different from coming back to review it, and only revoking my close vote when I actually think it's good enough.
The end results are:
- Questions that shouldn't be closed don't get closed. This will be the case almost always in the current system. Questions that get closed but wind up good enough get reopened.
- Questions that should get closed do get closed... but after a lot more time, and after making at least a few reviewers repeat their votes fairly often.