I recently purchased a new iMac desktop computer. Emails older than about two weeks seem to disappear. Further, all my old emails (from older iMac) were not "restored" to my new iMac. How do I address or solve these two problems--1) current emails dropping off after two weeks; and 2) restoring all my old emails to new iMac?
For the first question---------do you have the account enabled on some other device like a phone or tablet using POP3 instead of IMAP? If so it may be downloading the messages then deleting them from the server.
For the second question----------what folders on the old Mac are you referring to? Do you mean the default folders like Inbox and Sent and so on? Or the local folders that would appear under "On My Mac"? Were you running Time Machine with an external back-up drive? If so you should be able to restore everything from that.
Do the missing folders and emails show up if you just sign into the webmail UI using a browser? Also see here---------------