Are you using Gmail? and are you viewing the All Messages folder? The way Gmail works, when you have read a mail and delete it, it doesn't disappear from your account. It is just re-labelled; Gmail labels correspond to folders in Thunderbird. All of your Gmail messages have the 'all messages' label, obviously, so if you are subscribed to that in Thunderbird your messages won't disappear.

POP or IMAP ? Are they being actually being downloaded again or 'reappearing' ?

If 'reappearing' then there may be some corruption in your Inbox. This can occur if you are not compacting on a regaulr basis.

• http://kb.mozillazine.org/Thunderbird_:_Tips_:_Compacting_Folders

Please try this:

• Move all good emails out of 'Inbox' into other suitable folders for organising/storage.
• Delete any emails you do not want.

When Inbox is empty:

• Right click on Inbox folder and select 'Compact'.

• right click on 'Junk' and select 'Empty Junk'
• right click on 'Junk' and select 'Compact'
• right click on 'Deleted' and select 'Empty Deleted'.