Mail Password Required

[#1]

I use Mail on Mac. Since upgrading to El Capitan I keep being prompted for passwords for my email accounts. Apple say it's my ISP.
Any ideas how to stop it?

[#2]

A little Googling about this shows me you might not be alone in having such problems after upgrading to El Capitan.
A few posts such as this http://www.gottabemobile.com/2015/10/02/common-os-x-el-capitan-problems-fixes/ suggest that some settings might now be missing.
If you check and everything looks to be as it should be I'd remove all settings and set Mail up again from scratch.