Odds of Hanging On
Restaurants are revolving doors (especially places like the Cheesecake Factory, which have actual revolving doors), so a lot of hanging on is about who you know and who's willing and able to hook you up somewhere else when it's time to move kitchen.
Food is personal, and as such, many jobs related to making food are obtained via personal referrals. So don't expect you can treat everyone like Mr. Ramsay does and have everything be smooth sailing. You're going to want to make some friends in the biz.
Your odds of hanging on also have something to do with the type of establishment you're working for, and how good a chef you are. It's tough having to bounce from one place to another.
You may have to learn an entirely new menu (even if you have a bit of input on the dishes to be offered) and have to adjust to a new environment and new people. But if you're able to land yourself one of those cushy, secure chef gigs, then we like your chances. Food for thought.