After you posted I tried again - and it went right in to my Earthlink account - but only downloaded emails up to the day I first tried it (two or three days ago). I logged back out of Earthlink, then had to enter account/password again, and it was back to asking me for a Microsoft login. So, I deleted myMail and bought the full version of AltaMail. Still working on finding my way around on that. It (and myMail) are positively gaudy looking compared to Apple's Mail - they both look like K9-Mail on Android (which I have messed with because the default email client on my little Asus MeMO Pad tablet was confused about how POP worked as well - or at least showed some - but not all - of the same symptoms). But if they work properly, that's the main thing right now.
I have other things to do than just do self-computing-support and one of the reasons I (up to now) have preferred Apple stuff is so that I had much less of it to do. Grrrrrrrrrrrrrrr.....
Here's hoping 9.1 beta 6 reteaches Applie's iOS Mail app how POP emails work.
(for anyone who is curious - I got the MeMO Pad to just taste what Android was like - you never know when you have to do computing support for your kids. Since I got my iPhone 6+ late last December it hardly ever gets powered up.)