How many times can a champion return on Jeopardy?

Answer 1

For a champion there is no limit.

The Contestant who was a winner comes back until they lose. In a tournament a losing contestant can sometimes continue to play by earning a wild card spot.

A Champion is invited back to pay in Tournaments and chosen. They can lose tournaments and still come back and play in anew tournament or even be chosen for a wild card spot and continue to play in a tournament after they lost.

A champion like Ken Jennings can even have tournaments that are merely special matches created just so they are a contestant, like the Watson Match.

So Contestants can play until they lose, Champions come back based on a set of rules created by Jeopardy for an event or can just be chosen for an event.