Tip for administrators of Joomla powered web sites. 

Yesterday I was about to use the "Mass mail to users" function from Backend admin. But the mail could not be sent, I was notified. I have been able before.

After some reading and thinking, my best guess is as follows:
In Global settings > Server > e-mail preferences, I have used a e-mail address not related to this @mydomain.com. I changed the settings to an e-mail belonging to this @mydomain.com.

And now, it worked perfect to send the mass mail again!

I believe my web hotel has changed its rules, so it now must be a valid e-mail account related to this @mydomain.com.

So: use an e-mail account from same domain as your website.