I suggest they’ll be around indefinitely. While large customers are willing to spend large sums of money to maintain their systems and avoid the risks of new technology upgrades, IBM will continue to serve those customers.
My inclination is to agree but I work for a bank and we're in process of replacing all systems hosted on our mainframes. Will we ever get there is another question but that's the current road map.
Forever is such a long time. There are no new projects started on mainframes and there's a definite, if still quite flat, trajectory towards moving things off the mainframe. So eventually it will die, but it will be decades.
As we approach the limit (of zero) that tail will just continue to get longer and longer. And by “indefinite” I do not mean “forever.” I mean that there’s no definite date that the ‘mainframe industry‘ will end— IBM hasn’t published any roadmap to end their use, and many institutional users are happy making few changes to business operations.