E-mail accounts/incoming automatic delivery is not working/have to use manually send/receive

I have 4 e-mail accounts of of which show under "Tools" and "Accounts.  However, only two show a green light.  The default and remaining account don't show a green light, which they used to.  Both the non-green lighted accounts still work but don't automatically come and receive mail from those accounts without first going to send/receive, clicking on those two accounts and then the mail comes right in.  I have called the server for those two accounts and they have done everything they can to ensure that the mail should be automatically come in.  All mail can be sent out without doing a "send/receive" command on all 4 accounts.  On the grey bar inside Outlook, the two non-green light accounts are not showing but the other two are listed.  Any help/advice?  thanks...Coach Don