Can you see new messages arriving when viewing the account through webmail? If so, there may be a corrupted message blocking downloads.

https://support.mozilla.org/en-US/questions/1158670

Yes, I can see new Messages in my 1&1 webmailer but I cannot Download them to Thunderbird. There are no unusual messages in there, though...

Yes, I can See new messages in my 1&1 webmaile, but I cannot download them to Thunderbird. There are no unusual messages in there, though...

You wouldn't be able to tell if a message is corrupted just by looking at the content. Besides following the instructions in the link, you could also empty the Trash and Spam/Junk folders via webmail.

Select Help/Troubleshooting Information, click Open Folder to open the profile in Explorer, close TB, open the subfolder of the Mail folder that corresponds to the 1&1 POP account, and rename popstate.dat. When you restart TB, the Inbox for the account will be redownloaded and may include all the messages if the original popstate.dat file was corrupted.

http://kb.mozillazine.org/Popstate.dat#Deleting_popstate.dat

Genial! I deleted a bunch of emails from 18.-19. of August in my webmailer and it worked! The rest of my messages was downloaded !!! I am very glad that I did not have to hack the postate.dat, but I will try this solution for sure the next time I get stuck with this issue. Thanks a mill for your helpful support!