I recently had to wait two quarters to launch a product because the only person who knew what some cobol accounting program did was out on leave.
This is one of the many reasons many big corporations fail to innovate. It is very hard (near impossible) to implement new systems in an environment dominated by old ones (not talking only about software and hardware here, also organizational dynamics).
Many mangers in large companies, derive their status and power from a knowledge of existing business processes and procedures. Any substantive changes to those procedures obviously represent an existential threat to that position and they generally resist it, often very vigorously.
That being said, the problem isn't so much the COBOL language itself but rather that all the software written in it is connected to all kinds of database system, messaging systems(?) and whatnot, making it very hard to move to some non-mainframe platform even if a customer so chooses. Or to put it another way, it's cheaper to pay even the very high prices to IBM to keep on the mainframe track rather than to migrate.