Never having fished tournaments, I have never experienced burnout as a result of that. Having said that, I have experienced burnout from fishing before.
I lived in Florida for a while and moved back to Nebraska a few years ago. I learned how to target bass while living in Florida and was blessed to live on the coast where I could fish both salt and fresh water. I became very spoiled fishing-wise when I lived there, being able to catch huge bass fairly consistently and being able to fish for tarpon and snook.
After moving back to Nebraska, and again fishing our local waters, I became very disappointed with fishing here. I didn't catch bigger bass at all for a while and obviously there are no saltwater opportunities. I became so discouraged I hung up my rods for a couple seasons.
After that break, I came to the realization that bass fishing is bass fishing. They may not get as big here nor am I able to catch as many, but they are still here. And I like to catch them. I've been pretty gung-ho about it ever since that break. I do start to get a little burned out toward the end of the season, but I have found that if I take a day off during the week throughout the season to completely disconnect from anything fishing related, that helps. As does taking the occasional weekend off and not fish.