But that message comes from your server and it doesn't care what email client you're using. It's hard to see why your use of Thunderbird would have any effect.

Have you looked at your email provider's webmail portal to check if these messages are there? I'd wager they are not, since for whatever reason your server has declined them.

Try sending these people messages and having them reply to your message. That would guarantee that they use the correct email address.

Thanks so much for your reply. I've had them try what you suggest with replying to an email, and the messages are not arriving to my inboxes. This is affecting 2 different email addresses that are on 2 different hosts; one is a Gmail account and the other is through my web host. And although I've had both of these email addresses for several months, I never experienced problems until a few days after installing and setting up Thunderbird. You are right that the messages didn't arrive into my email provider inboxes either. It's just pretty fishy/coincidental that 2 unrelated email addresses would be acting up at the same time. Any thoughts?

The Mailor Daemon "mail undeliverable" message usually has a bit more info which can help to identify what is going on. You would need to get a copy of that message in order to work out possible issues.

Do you use POP or IMAP mail accounts?

Have you used up your quota on the server? check this now. If you have used up quota then server cannot accept any more emails until some space is freed up.

Perhaps the sender has been flagged as an email address, IP address or using a server that is sending out Spam and your server is rejecting it.

Test: As you have more than one account, can you send yourself an email from one account to the other and vice vera? Are these emails received ok?