All three should be on imap then. If one is on POP, that can cause problems like what you are seeing and it should be changed to imap to be like the others, for the same email account.
Without going into a lot of technical detail, imap is used where the email server (e.g. GMAIL, MS-EXCHANGE, etc.) keeps all the emails physically, and you view them on your local device, which can also keep a local copy. But the emails are retained on the server at the email provider facility. POP is different -- with POP, the emails are physically copied to your local device, and are deleted from the email provider facility based on how you configure each POP device. Delete one week after downloading is a common POP setting, which is why I was asking.
If all your devices are imap, and you see no settings on any of them that either deletes mail after one week or puts a limit on "sync" beyond 1 week (iphones are sometimes configured to show emails only going back 1 week), you may need to log on directly to the email server, say with a web browser, to see what is there. The process may be different with different providers, for GMAIL one goes to GMAIL.COM and you log in and can see all the imap emails, which should also match what is on your local devices using imap.
You never indicated what your email provider is.
Check your DELETED or TRASH folders for mail on each devices. Also check all your mailboxes carefully to make sure you aren't missing one that has the rest of the emails.