Please understand, it is not thunderbird, but the network of your email provider. Thunderbird attempts to save, but it is refused. This isn't a common issue, so I would focus on your email provider's network — and I won't be surprised if they swear their innocence. Good luck.

David - thanks for answering!!! Yes, they do indeed swear they are innocent. They said it was probably Thunderbird, and if not call Verizon (our ISP)... And they use as evidence the fact that when I access thunderbird on the server via a browser when I'm away, then all sent items are automatically saved. Are you sure there is nothing else to try for Thunderbird?

You cannot access Thunderbird on the server via a browser, although you can certainly access mail. What I mean is that the network path with webmail (for all email providers, not just this one) is different from the process when using an email client. Email clients (not just thunderbird) are forced to use the servers and settings provided by the email provider. Yes, you are impacted by your ISP and also by your email provider. Thunderbird is only an agent, attempting to send mail to the network. Good luck. :) You can try going to the advanced server button on 'server settings' pane for the account and reduce the number of settings, but that is, at best, a compromise with a poor network connection. Good luck. :)