Same account?
Is the phone set up as a POP3 account? Did you forget to tell it to NOT delete emails on the server? If that's the case, retrieving an email in the tablet deletes it from the server, so the PC can't see it.
If you're using more than one device on the same email account, make sure they're both set as IMAP, not POP3, for incoming mail. (Outgoing mail is still SMTP.) Then you control when the email gets deleted.