Secondary email account no longer working

A week ago my secondary email account stopped working.  I deleted it and installed it again in my Apple Mail on MacBook Pro (10.9.5) but it just keeps asking for the password which is what started it all, asking for the password.  I also rebuilt Mail and reindexed it. Useless.

It's still listed on the verizon website but no emails come in. It can't be deleted either which is very strange.

I sent an email to it from my primary account but did not even get a message saying it could not be delivered.

I tried calling verizon but that was totally futile, holding for 30 minutes, then was cut off.

I would be so grateful for some help with this.