SBO

No, I am sure nobody in the entire history of the airline industry ever thought that high availability systems might be a good idea. It's a good job there are people like you around to point us in the right direction.

In fact if the facts are accurately reported and both internet and airport check-in were down then it is likely to be a failure in the back-end passenger services system of one specific airline. In general these are airline-specific rather than utilities provided by airports (although there are exceptions). These back end systems have typically four nines availability or better although there are variations between the mainframe systems used by traditional airlines and the .NET based Newskies used by Ryanair and others. Life gets more complicated when check-in is being managed by a ground handler rather than the airline itself although that isn't likely to be the case here as a ground handler's system failing would not have affected web check-in.

It is also extremely unlikely that anyone at the airport would have been in a position to "reboot" the system even if they had wanted to as check-in systems usually live in vendors' data centres that are often not even in the same country.