POP3 mail does not play well with multiple devices, period. The standard was created when almost every one accessed their email from a single computer. The extra stuff that Mail and other apps use to get around these limitations are kludges that are apt to break if anything unexpected changes on the device.
The best solution, when available, is to use IMAP or Exchange servers. They are far more robust, being designed for multi-device reality the mobile world. Unfortunately, not all ISP's provide IMAP, which is one of the reasons I discourage people from using an ISP provided address as their primary email.f
The other reason is that if you move or change internet providers you're likely to lose the email address as well, and spend a considerable amount of time fixing all the many site and service logins you tied to it.