I'm happy that the community decided to reopen a question I asked on P.SE that had previously been closed, but I notice now that there are starting to be close votes again. Will there be a pitched battle? How long can this go back and forth?
It can go on for as long as there are people with over 3,000 reputation who haven't used their votes.
On any given question you are allowed to vote once to close and once to reopen. After that you can't vote any more. So any particular user can't vote to close (or reopen) your question twice.
Diamond moderators can vote any number of times.
Perhaps you should be looking at the question to see why it's attracting close votes and edit it so that it's a better fit for the site. That way, once reopened, it stays open and a valuable resource on the site.
Just for giggles, here's a quick summary of the number of users with more than 3,000 reputation. I used the leagues as my source for these numbers.
Total Rep* Users
I don't know how to / don't have access to "active" user counts to refine those numbers.
From the question's revision history, a total of 10 users have voted to close and 5 have voted to reopen.
So the "battle" could wage for quite a while.
I've locked the question in question. It was closed once by 5 community users, reopened by 5 community users, and closed a second time by 5 community users - all of this without any moderator intervention. It's being discussed in this Meta question, and so far no one has provided an answer to suggest that such questions are on topic.