Worst case, with good weather, you can stop service for a few days: day 1 mandatory rest; day 2 fly crews to where they need to be to start service; day 3 mandatory rest; day 4 return to service. Then start rebooking passengers and picking up the pieces. Carriers with long haul international may need longer, and maybe you need more rest days to ensure everyone is ready for their normal shift, but that's a reasonable napkin estimate.

Otoh, Delta seemed to have recovered after about a week, and canceled about 1,000 out of about 4,000 flights for several days. It's way better to fly 75% of the daily flights than not. There's less wiggle room in a summer schedule for weather, but there's still some wiggle room.

There probably is an upper bound on down time, by which point the business has suffered some irreparable harm. It might not result in the business simply folding, but might result in significant expense or legal complications, long-term reputational damage, etc. In business continuity speak, that's the "maximum tolerable downtime," and while I don't know how Delta defines it for the impacted systems... I imagine they're not happy with how long they were down.

They did a "reset." Cancel enough flights to reduce load, then manually recalibrate the crew tracking software to figure out where everyone is and their hours. Then start operations again.

It's like stopping your in-place manual software recovery efforts and restoring from backup. You KNOW it's going to take a massive amount of time, but at least you know how much time it's expected to take, and what the expected result is, rather than "2 more hours... 2 more hours.... 2 more hours.." for a week.