Apple Mail not working properly
Apple Mail has a wonderful connection doctor.
I would open it and see what specific error it finds and then work to solve it from the wizard steps and help that the connection doctor provides for your specific setup and mail provider.
Once you've done that or if you can't solve it - then you can ask a follow on question or reach out to that mail vendor's support with a very specific error condition and not just "mail doesn't work"
- Click the Window menu
- Click the Connection Doctor item
- Follow the results for any light that's not green
Probably it's because of using POP3 as incoming mail server, switch to IMAP to insure that the message will arrive to all of your devices not just a single device. Check this question.
POP3 and IMAP are two different protocols (methods) used to access email.
Of the two, IMAP is the better options and the recommended option when you need to check your emails from multiple devices, such as a work laptop, a home computer, or a tablet, smartphone, or other mobile device. Tap into your synced (updated) account from any device with IMAP.
POP3 downloads email from a server to a single computer, then deletes it from the server. Because your messages get downloaded to a single computer or device and then deleted from the server, it can appear that mail is missing or disappearing from your Inbox if you try to check your mail from a different computer.