I did some digging by firing up Gwibber in a terminal:
$> gwibber-service -o -d
This is what I got:
Gwibber wasn't refreshing because it was timing out on the DNS lookup. I have Verizon FiOS as an ISP. FiOS having terrible DNS seems to be a problem. I switched over to Google DNS and every thing is snappy and working properly. If you're using Gwibber on FiOS and having issues, try this out. It may save you an hour or three.
Gwibber, or whatever library it is using for network communication, picked a pretty short timeout, but this is pretty lame. Verizon really needs to step it up here. People will perceive FiOS as slow because it takes forever to look up an IP, even though the network is pretty quick in my experience.