My local library isn't open at 6am either (opens at 9, or 10 on Sat and 1 on Sun), and closes before 7 on Fri-Sun.
> someone needs to
Do they though? Why is there some assumed urgency? What happens if they don't do it "whenever they feel like it" (e.g. normal hours)?
Computers also generally don't randomly just stop working, and if they did in this case (network engineer), it's almost certainly the ISP anyway.
Archive is likely one of the top traffic destinations on the internet. Your local library is likely not.
Maybe they want to hire someone full-time is so they don't have to have a policy of whenever they feel like it?
Having a reliable service is likely one of the reasons why their donors donate in the first place. Why do organizations and wealthy people still want to donate if the service goes down for 2 days and no one cares? Why would this kind of non-profit attract top volunteers in the first place?