Hi - I'm happy to help with your Mac issue. Please remember to Accept when we are completely finished and you are satisfied with my answer. The iPhone is apparently not releasing the lock on the account. I suggest that you switch to IMAP protocol if supported by your email provider. When accessing a mail account by multiple devices POP often has problems - it is an older, less capable method, and will often create sync problems. IMAP, on the other hand, is designed for multiple access and will always keep things synced as the mail lives on the server - not on the local machine. If IMAP is supported, I urgently recommend you switch to it.
Be sure to back up your local mail on the machine using POP, particularly your Sent Mail as once you delete the POP account, local mail will be deleted. You can probably set up the IMAP in PArallel, and then copy any mail you want to save to eith local folders or back to the imap server.