There is an interesting post on this. I have to restart mail every 20 mins if I want full email functionality. I forward several email addresses to a gmail account as a way of backing up email. It seems to be (not 100% sure) this arrangement that makes all accounts go offline regularly, or at least say they are. Strangely I can still send all, and receive some email. I keep meaning to knuckle down and fix it once and for all, but I dislike email so much that I can't bring myself to invest time in it. So I keep wasting time.
http://tidbits.com/article/14219