Hi manellop,
Thanks for using the Apple Support Communities! I'm sorry to hear you are having this issue with your mail. I'm a bit unclear on your exact configuration; do you have multiple email accounts with the same provider, multiple email accounts with multiple providers, access one or more of the accounts from multiple devices, or some combination of the above? In general, the biggest difference between IMAP and POP is that IMAP leaves everything on the mail server (like a message board), while POP downloads the mail directly to your computer (more like the post office, which is where it gets its name: Post Office Protocol). This means that if you have two different devices set up to access the same email account via POP, they may only get certain emails and miss out on others, just like two different people fetching mail from an actual postal mailbox.
Some mail providers may allow POP accounts to leave mail on the server, but sometimes only for a limited time after it has been initially fetched. If you are using multiple devices to access an account, you may want to use IMAP for all devices. If you want to remain using POP with multiple devices, then I recommend taking a look at the support article linked to below for assistance.
Get help if you have issues using a POP email account with more than one device
Regards