I would say it depends on on staff discretion but there is no explicit criteria. The issue with a 50%+1 majority is that you can have users who didn't vote complain that the "poll period" was intentionally cut short to prevent them from voting. So my guess is staff will want to see something more significant than a simple majority.
A community discussion should have a clearly set deadline by which to respond before. Should an admin/crat interfere with it by blocking and deleting, then Staff can be called on to oversee the integrity of the discussion.
Technically, since only FANDOM staff can demote a bureaucrat, the criteria is whatever convinces the FANDOM staff person. Beyond that the local wiki can make any process it likes, but if it doesn't convince the FANDOM staff person handling the issue, it is sort of irrelevant.
So, if you want the most meaningful answer, you should ask FANDOM staff if they have any internal guidelines they use for doing the demotion at "Contact us".
All that said, a vote among the active community seems more fair... as many folks like to say, admins shouldn't be given too much special treatment just because they're admins (although I somewhat disagree with this perspective). If they are persuasive, that should count more than because they are an admin.