I had tried to put a host into maintenance mode so I could reboot it. But it seemed to get hung up, but I didn’t see any outstanding tasks, so I just rebooted it. After it came back up, things seemed alright, and I started up the various VMs on it. Later, I started a migration task to change the storage of one of the VMs on that host. At the very end it said “the operation is not allowed in the current state” and failed. It happened again when I tried to deploy an ovf template to that host.
This post from VmWare gave a number of things to try. For me, it was disconnecting the host from vCenter and then reconnecting it (all right-click operations, so it was easy and quick). When it reconnected, the host was shown to be in maintenance mode, which was not the case before disconnecting and reconnecting it. Things seem happy now.