I could see why people would stick with it. It's a relatively low-stress job that pays decently, has government labor protections, government benefits, and doesn't require a lot of education. Some searching suggests the average pay of a TSA worker is $56k. Plus retirement and health insurance. And the only credential required is a high school diploma or a GED.
What other job that requires nothing more than a high school diploma has pay and benefits that good? Maybe if you start your own business up. But in terms of wage labor, very few things come as good, at that education level, as a TSA job. A couple, each working at the TSA, can easily bring in $100-150k per year if they stay there awhile.
It's quite understandable why the TSA agents won't quit during a shutdown. When the money is flowing, being a TSA agent is a pretty decent gig.