I'm not sure exactly what's triggering this problem, but I've had three extensions disabled for about two weeks. For all three extensions, when I click "Delete data" I'm brought to the confirmation page (with the red banner). When I confirm, I see the green banner confirmation that the extension data has been deleted. When I go back to the extension list, the extension is still in the disabled category, but it just says "Enable".
I've tried enabling, disabling and trying to delete it again, but that doesn't work. I don't think it's a cache issue, because for unrelated reasons I've cleared the cache multiple times this morning. I've tried it with my FTP client open and with it closed and that didn't matter.