I would note that, number one, in a minority Parliament, where the opposition members would vote out a committee chair, they would also have the majority of the vote in the House. So unless it would be impossible for them to find another government member to run for it, they could basically choose who they would want for that chairmanship.
Now, it's very possible that the government caucus could sit together in complete solidarity and renominate their candidate. There could be a couple of solutions here. You could have the endless loop possibility, or you could have something where, if someone is deposed two or three times, they're just gone—the three-strikes-you're-out rule or some version of that.
I would be reluctant to ban whoever is deposed as committee chair from being able to run again, because sometimes after motions are passed or disputes have reached a certain point a resolution can be found. People may want to make their point and then be happy when they have the committee chair back. Sometimes they may not so much want to remove the chair as send a message, and the message might be sent. So it's possible that a recommendation could be that if a chair is deposed twice—just to pick an arbitrary number—or three times, he would not be able to stand for re-election.
If your report wanted to go into that sort of detail, I think it would be appropriate. Hopefully that situation would not arise, but a two- or three-strikes-you're-out rule could be a possibility.