"Can this be resolved "
Yes
"are XP and 7 incompatible in this regard ?"
It has nothing to do with Windows XP and 7. It's becuase the defualt behaviour for e-mail clients is to request that the server delete the e-mails once they've been downloaded.
On each of the machines, you need to go to the account properties, go to the advanced tab, and check the box "leave a copy of messages on the server". Then set a delete period that will encompass the max period that's likely to elapse between one machine and the other. The idea is that you want the messages to remain on the server long enough that they can be collected by both clients, but not so long that they are likely to cause you to exceed your allocated storage on the server.