It would be pretty rare for it to be a hardware problem if the servers are up and running for a time, then go down or (not respond) for a while. (I worked occasionally on network and LAN support in a past life).
I noticed that the servers (including the main website) go down from time to time, but never seem to completely fail (the old phpbb did give the occasional critical error though). Check your load balancing first, then your raid setup… as both of these can severly affect performance (ie… network traffic) if configured wrong. Once when working at a small company, when a backup was running, ALL access, whether network or internet slowed to a crawl.
There are possibly other network issues like the age of the network software that controls group policies and permissions, email and remote access.
From personal observation I’ll see all performance die on almost a daily basis. So you might be able to find a pattern, and check to see if anything is scheduled to run at those times.
(I hope I’m not being too invasive. I’ll always have a little tech support in me.)