Sounds like you have to e-mail account defintions checking the same mailbox.
(especially noticable if you choose to leave mail on the server when working
with pop accounts.)
I had this problem as well. It turned out to be a rules
problem. Check your Tools - Rules Wizard and look for a
rule with moves a copy of incoming mail. You want to move
the original.
There are a number of variations on this theme, but the
culprit is generally the Rules setting.