* The web site is tied to an old fashioned batch system/mainframe that doesn't run in the same mode 24/7. Yes, the implementors could write a separate queue that managed this - but that would be often be a non-trivial amount of work.
* It's for a system that provides the online equivalent of an offline process, which has escapes that occasionally push the user out to talk to a human being. The human's aren't available 24/7.
* It's for a system that provides the online equivalent of an offline process, and there are legal or social requirements that the applications be "fair" - i.e. that the people going through the online and offline process should have the same opportunities. Having the online system run 24/7 puts people with online access at a significant advantage.
They also said their analytics showed that no one ever visited the site outside of business hours. This wasn't what I was contracted to do (and I wasn't in position to fix it), so I didn't bother to tell them that when they shut down the web server their analytics stopped running as well.
If you (effectively) subdivide your content pages from your processing pages (on a separate system), you can simply take the latter down.
It may not be ideal for today's idea of a 24/7 world. But if you're small, geographically local, and want your staff to have sane lives, it's possibly one approach to consider.
(And there are currently arguments circulating for reinserting some sanity and balance into the way we live our lives and jobs.)