I had this problem too but I fixed it today.
Go to the mail menu preferences.
Click on account in question.
Select the outgoing SMTP mail server (the one offline), this has a drop down list, click on the edit server list.
Click on the advanced button.
Make sure use default port is checked.
Make sure SSL is unchecked (unless your provider requires it, mine does not work with it checked).
Have authentication set to password.
User name should be your email address for that account.
Make sure correct password is entered (for some strange reason my password box was blank on this account).
Push the ok button.
For me the SSL box was checked and the password was missing. This is strange to me considering I have unchecked the SSL Box on the mail preference advance page. Also, I went through the complete set up account when I first created the account, why was my outgoing server password box empty?
I hope this helps.
Here is a link to some visual aids with the steps from my ISP
Your clear and uncomplicated step-by-step instructions are refreshing, and enabled me to solve my issues quickly.
I visited many other threads on Apple Support, and to my frustration, I found they are often clouded by confusing technical jargon and 'off-topic' banter from geeky know-it-all's.
- Keep posting!
The Modern Designer