Let's say you have a question that was marked too broad and it was voted closed. When it is reopened, can it then again be voted closed?
After a question is reopened, it can be closed . . . and reopened . . . and closed . . . and reopened . . . ad infinitum, really. People do run out of close votes, though, so you can't have two groups of five people fighting each other to close or reopen a question. Other community members have to vote, too.
Closing and reopening does have a small element of subjectivity to it, so this thing does happen, sometimes after various edits have been made, and sometimes because people just don't agree with each other.
You might want to flag for moderator attention if a question goes back and forth and back and forth like this a couple of times; that means there's probably a dispute that needs to be settled. Raising the issue on meta to try and get a community consensus is also a good step.
Sure. Though at some point if there's multiple opens and closes, someone needs to take a look and work out what we actually need to do
I think Joel's post on meta.so is an extreme example of this, so it certainly can happen.