Q: MD5 Challenge-Response, time-outs

For the past 2 weeks or so, mail.app is killing me. Upon relaunch of the app, it collects mail once, then times out on all other mail collection until I quit mail or reboot. Anyone else having this problem?

Here are all the facts I can think to share:

I have 4 email accounts in Mail.app: one iCloud, my own domain hosted for years at the same top notch place, and two gmail accounts.

I have tried changing the Check mail frequency, but that doesn't help.

I have tried disabling the gmail accounts and even the iCloud account. This doesn't seem to help the time out issue.

One very odd thing is that for my own domain's  email address, I have always set my incoming mail verification to Password but now I see the app repeatedly sets it to MD5 Challenge-Response. I change it back to Password  and always save my change, but next time I check Mail Prefs, it's back to MD5.

I have check with my email host and have verified that my settings are correct.

I have heard that Mail.app hates SSL. Could that be the case? I've been using a cert and the same settings for years and this has never been an issue.

This problem did not start when I updated to El Capitan.

This did not start when I came to live where I am now.

I had no crashed and installed no other software. I have turned off the few apps that launched on startup: SnapzPro, Viber, and 2 utilities. That didn't help.

I have made sure I don't have duplicate accounts in Sys Prefs, Accounts.

Email still goes out, although perhaps more slowly, maybe because mail is busy trying to collect mail. My problem is ONLY with incoming mail and I can't help but suspect it's the MD5 Challenge-Response issue.

Messages often don't move to the trash or junk folders, except sometimes when I move them immediately after relaunch.

Trashed mail returns upon most restarts.

Oh, one more thing: for weeks and weeks now, Mail app has been crashing at least once a day, sometimes even when it's just in the background. (I have reported each crash.)

The mail app was already close to horrible because it insists on checking all accounts at the same time. (I have begged Apple to allow different schedules the way Outlook Express did, ever since day one of this app but this seems not to be on Apple's radar.)  But it managed. Now it is virtually unusable. 

The only other thing I can add is that the wi-fi on this MacBook Air has always been really, really poor, everywhere I have used it, which is many locations, many countries.

I know all about creating a new user to test. I could possibly delete and recreate my account, but don't really want to. I don't know if anyone here will be able to help but I would like to know if anyone else is having this problem.

Hope to hear from some of you soon.

Thanks.