Just a shot in the dark, but I wonder if everything on the server end shows to have already been downloaded and you will only get new mail on the NC.
I have not personally done anything with the email app, but I wonder if there is a setting, like in Outlook, to leave mail on the server for x days. If so, the first device that gets mail doesn't leave it in a state where other devices are not able to receive everthing that's currently on the server also.
And if it's not POP3 then it's IMAP, and it always keeps your emails on the server unless you delete them.
The email app syncs with the server everytime it gets mail. There is a twist however. Lets say you had previously downloaded email to your NC and then downloaded it to your PC which then deleted it from the server. The next time the NC syncs with the server it will download new email that is on the server but it will also remove from the NC the previous emails you downloaded but are no longer on the server.
In short, if it's on the server, it's on the NC, if it's not on the server, it's not on the NC.
The only way I know to stop unwanted deletions from the NC is to change your PC email settings to not delete email from the server. Either for a set number of days or until you empty the Deleted Items folder.