Can you confirm your account type - POP or IMAP?

I'm using POP.

With POP all mail is downloaded to your local disk. You can tell Thunderbird to leave messages on the server though. Check your account settings whether this option is enabled.

What is the exact error message you get?

The message is from admin and the subject line is: ATTENTION: Bounced Message Notification, bytes in mailbox!!

The body of the e-mail is:

A message was sent to you that was returned to the sender(bounced) because it would have caused your mailbox quota to be exceeded.

The following is the reason that the message was over quota:

      Quota Type: bytes in the mailbox
 Quota Available: 2504803
     Total Quota: 102400000

The following is the information on the message that was bounced:

     Sender: Mail Administrator <Postmaster@socal.rr.com>
    Subject:  Mail System Error - Returned Mail
       Size: 13473366
 Message ID: 962a105c-ca7c-11e4-9d27-89f8d2c46959
       Date: Sat Mar 14 19:01:57 2015

   Reply-To:  <Postmaster@socal.rr.com>

The message was bounced from the following folder:

   INBOX

To fix this problem, delete some messages from your mailbox, and contact the sender to resend the message.

If the size of the message is too big, contact the sender to reduce the size of the message and resend the message.

Since you confirmed your account is POP, all messages should be on your local disk. Login to your account via webmail, and free up space on the server.

Just a mo; how do you KNOW the account uses POP? It seems to be behaving like an IMAP-connected account.

I looked under the Tools menu, clicked account settings, then clicked server settings. Server Type was POP Mail Server, server name was pop-server.socal.rr.com.

It looks like I was telling Thunderbird to save messages on the server. I'll turn that off and clean out my Time Warner server.

Thank you for all your help.