As most of you have noticed, we've been on the new server for a few days now. There have been a couple hiccups, and the router also decided it wasn't getting enough attention, but I think we're in a good spot now.
As far as the web interface staying up and incoming mail being delivered, I would agree. Outgoing mail, however, is just not reliable. Sometimes it works and sometimes it doesn't. I am not seeing a specific pattern and it does not seem to be related to mail addressed to any one particular domain. I wish I could provide more clues.