Relaying disallowed as My User Name

Relaying disallowed as My User Name

We have 3 computers monitoring one account. 

One of the computers gets the above error from time to time. The email gets moved to the sent folder in the client (Thunderbird) but the email is not sent.

This is causing customer service failure!

Please help to sort this out!!!

I have checked all the SMTP settings. Its most anoying!!!