10.14.4 killed my IMAP email accounts

I have a suggestion. Go to Mail/ Preferences/ Server Settings. Enter your mail account password in both the Incoming and Outgoing Server fields if they are not already there. I have had this work for me in the past, maybe it will work for you.

I had the same problem- the upgrade stopped email coming and going-- changed my mail account to iCloud mail as outgoing and incoming mail, deleted all other mail accounts-- it worked- I now receive my gmail through the iCloud account--hope it keeps working.

Trust me when I say that you are not alone. If you read the ASC forums regularly, you will see that a lot of folks have been having some major email issues -- and major problems with other apps, such as Time Machine and Messages -- since upgrading to Mojave. I am so thankful that I have been spared, and that everything continues to chug along smoothly. Hopefully, Apple will work out all of the kinks in upcoming releases of macOS. A lot of people appear to be frustrated right now. But just hang in there, and it will eventually work out for you -- even if your hair turns a little grayer in the process. :)

Look at the IMAP settings and see if the field (in Advanced) "IMAP Path Prefix" has been changed. I recently deleted my mail account to rebuild on IOs phone and the new account rebuild put in / for the prefix setting. My mail provider requires INBOX (all caps) as the setting for IMAP path Prefix. Until i fixed this, it would not connect with the mail server. Maybe you have this issue? Good luck..

DD