Work on a dual Java/COBOL team in a F500. Not a COBOL dev myself but I'm surrounded by them. Two biggest problems are:
a) the systems are very tightly coupled, like uber-monolith architecture, and it's hard to QA them without end-to-end testing through everything. Good luck getting anyone to refactor them because a1) they're going away and a2) they're so huge. Which leads into . . .
b) there's 40 years of undocumented business logic in there, or business logic that only exists in code comments. And it still makes billions of dollars a year. So good luck replicating 40 years of tribal knowledge in the new systems.
c) It was written by cowboy coders 40 years ago when the company was a startup, so no one can learn to work on it without first getting hired here. The joke is one of the original architects went and created his own dialect of COBOL.