Mail keeps asking for my password and doesn't connect to the server

When I open Mail, it asks for my email password, which I enter, but then it keeps asking again and again and doesn't connect to my email providerr's server. The provider says that the issue is a "known problem" with Apple and that the problem is on Apple's end. Apple's on-line help says it is the email provider's problem.

and yes, I've changed my password and entered it correctly several times and Mail is still not connecting to the server. I have several email acounts with this provider and all the others work fine, just this one - very critical one - that does not.

Help!