Why? (Asking as someone running Arch on many servers for the last 5 years, and debian server for much longer)
I can think of a few things I dislike, but all of the failures so far were self-inflicted. Like forgetting to update packages that I self compiled outside of supported repository.
It's not completely autonomous when it comes to upgrades, you have to think for a while before hitting "yes" after seeing the list of packages to update, but so is not Debian in the long run... (some of the servers I have to manage are 13 years old or so, and going through major dist-upgrades is never that pleasant either. It's a bit more hassle, because I don't trust the major version upgrade so I have to run them on a backup VM first just to see whether some issues will crop up).
But having the latest versions of the programs is great, I don't have to second guess myself when writing new programs (will it be compatible?), can use the latest kernel APIs, etc.
This is all personal experience, so obvious salt is required with it.
I've had bizarre networking bugs pop up on arch that I've not had elsewhere. I also just don't like rolling releases as much as I used to. Since the majority of what I do can be containerized, I prefer a much slower release cadence for my hosts, and anything that requires more up to date packages just gets thrown in a container.
Basically, I think my server workflow just doesn't line up with how arch works. On desktops it's great, since I'll always have up to date video drivers, desktop environments, etc, but on a server I don't usually use things that require the latest and greatest software. I figure as long as it's still getting bug fixes, I'm probably fine.
Arch changes too much, and change means risk. In my opinion, for production, boring is always best. If the latest flavor of X is absolutely essential for the business, there are typically ways to get it for most LTS distros (back ports, third part repos, etc).
It also changes in ways that can make it hard to automate deployments. For instance, the base package group used to include a kernel, but no longer does.