Stress
Every job has a certain level of stress, and it typically depends on how quickly and perfectly other people need something done. With archiving, there isn't usually an ASAP quality to the work. It's finished when it's finished, and not a second earlier.
There's more stress involved when you're dealing with something of historical significance. If you're entrusted with the preservation of the Declaration of Independence, you might get a couple butterflies in your tummy.
There are also specific stresses to particular specialties. Most archivists aren't on a deadline, unless they work in a newsroom. Film archivists may have it the worst, especially if they work in a studio, because producers can be strange and demanding people who want it when they want it. They may end up the bane of your existence.
In academia (which is a fancy word for "I work at a school"), people will come to you for help researching their projects; but even that's not too bad. The operative words here are their projects―you don't really have anything on the line there.
While it varies depending on the working conditions in your particular archive/vault/cubby hole, stress on average is minimal for the professional archivist. Just about everything you'll work with has already happened; you're just putting it away in a place where people will be able to get to it later. That may be why just about all archivists report personal and professional satisfaction in their jobs (source).