I'm having similar problems. Again. It's been a persistent, sporadic issue for *YEARS.* I've been a Cox customer for just over 20 years, and I'm nearing the end of my rope.
I changed my server settings back in February to reflect the new security measures and updated my passwords at that time. Everything worked okay until last week - a whole 9 weeks without a problem! Woo-hoo!
Last week, my phone began having trouble connecting to the email servers, continually prompting for my password and refusing to retrieve messages. The same began happening on my desktop at the same time. The phone has quit doing it, but my desktop continues. Sometimes it doesn't even accept the password, and I'm just forced to go without my messages for a while.
Nothing has changed on my end since I updated the settings and changed my password to the required settings.
This is ridiculous. I'm slowly migrating all my email subscriptions to Gmail; when I'm finished with that, the only thing keeping me with Cox will be the dearth of competition in Internet service providers. Once that changes, it'll be a struggle to justify my continued patronage.