email problem - update serial # zone??

Hi
I have two websites that keep having trouble emailing each other. Actaully one is mine, one is my associates. They used to be on the same server, now one is on a new server so they one that stayed is looking "locally" for the one that's moved and unable to find it. (excuse my lingo or lack thereof). My hosting provider fixes it but it recurs about every month or so. The first site is
centralmaine.org
server ip 66.195.19.200
(that's my dedicated server)
the second one is affiliatedrlty.com
and it is on a server named dime24 so it would be dime24.dizinc.com I believe.

The hosting provider, hostdime, instructed me to update the serial number in the zone file on centralmaine.org but I'm unsure what that means and how to go about doing it, and IF that will really solve the problem. Any thoughts? I'm thinking I've given enough info but let me know if you need more. Thanks so much!