Yeah... 90% of the "Mission Critical" calls that I get are BS. I do IT work for a development and test lab, and my customers STILL rant and rave every time I have to take down a server during business hours.
Anyway, I usually get into one of those situations once a day:
Whining Developer: "My application/server is down! Can you reboot/restart it for me?"
Me: "No, I'm in the middle of installing some security hotfixes/software upgrades/hardware upgrades. It will be back up soon. Didn't you get the note that I sent about this last week?"
Whining Developer: "But I'm in the middle of coding/testing/deploying unimportant/marginally important project X! I need to use the server NOW! Why can't you do this work later?!?"
Me: "No. This is a test and development lab. If you want 24/7 off-shift support, you can get your server moved to the production server room for $$$$$ dollars. (It's easily 5X what I charge) Would you be interested in looking into that?"
Whining Developer: "Ummm.... yeah. I'll have my boss look into that. Please let me know when the server is back up."
I hang up and smile. If the customer was particularly nasty, I'll make sure to time my snack break to start right before the server is finished
Occassionally, I'll get a complaint from the Whining Developer's manager, but their unimportant/marginally important project usually doesn't have the funding to get 24/7 support. My customers are stuck with me, whether they like it or not!