Only two of 6 macs on network allowed access to IMAP mailbox

Allright, our main email at my office is set up as an IMAP address on the entire network (2 macpros and 3 iMacs). None of the iMacs can access the email. It will just repeatedly ask the the password over and over again. It will update the email for a brief second after a "failed" password attempt (even though it is the correct password). On top of that, on the two macpros that it DOES work on, I occasionally, for no reason, see that the email address has been "disabled" in my mail preferences and I have to enable it again. And I have to reload my signatures about 20 times a day. Please help! oh yeah, the program is obviously Mail.app.