The only thing you do by keeping things running through heroic effort is to send a message to management that they can lower the priority of dealing with the issue.
Managing upwards (getting management to make decisions in your favor) means that you can't let yourself be the reason they don't feel the pain of a problem like poor staffing. Sure, you can step in and save the day if you really, truly, need to build up your reputation as dependable/hero, but it's a thin thin line.
One thing I often do as well is try to look at people in other departments and their general attitudes towards time off, vacations, having to leave for Dr's appointments, that sort of thing.
I'll be damned if I'm going to live in a constant crunch time situation, feeling like I need to take lunch at my desk, and put off things I need to do for me.
Especially while other teams are having regular team building outings during work hours on the company dime, one guy takes a long lunch and to go to the gym, and two others were clearly taking the video call meeting while out walking their dog.
Everyone deserves consideration of the fact that they are human, and everyone deserves the kind of flexibility that often is only for business side "important" people.