I think this is when a manager is supposed to add resources. I don't accept the idea that it should be normal for everyone to have to work ridiculous hours until the crunch is over.

It's the manager's job to make sure there is slack in production; that there are resources available for emergency situations, and that there is enough redundancy built into the production team that if somebody gets sick or somehow can't work a normal workload, somebody else can pick it up. If a crunch situation is unavoidable, as a manager, I would be deeply apologetic and appreciative of my employees' sacrifice, while frantically searching for a solution to ease the burden. If I can't bring in help, I need to adjust the scope or push back on the deadline. Plain and simple.