DKS, I use Thunderbird, and I UNCHECK leave messages on server which is what I think you meant?
TB will also show you WHERE the e-mails are stored in SERVER SETTINGS under ACCOUNTS. Click BROWSE and go UP 3 levels. If you see more than ONE PROFILE, it is possible your OLD e-mails are in the other profile.
It might be here, where 'irv' is your USERID.
Volume in drive C is OS
Volume Serial Number is 1C5C-DD5E
Directory of C:\Users\Irv\AppData\Roaming\Thunderbird\Profiles
10/29/09 02:41 PM <DIR> .
10/29/09 02:41 PM <DIR> ..
02/23/13 09:33 AM <DIR> d2tufje1.default
12/02/11 02:18 PM <DIR> dpt58nel.default
0 File(s) 0 bytes
4 Dir(s) 45,667,905,536 bytes free
As you see above, I have 2, one from an OLD computer with old e-mails kept for archive.