Can not download large messages
From MozillaZine Knowledge Base
Most e-mail providers limit both the maximum size of a message and a message attachment that you can send or receive. Their web site should have a support section that states the limits. If it's a binary attachment the attachment is approximately one third larger due to base64 encoding. You might consider having the sender use a file splitting utility to split the attachment into several files, and send them in several messages. You'd need to download a copy of the same file splitting tool to re-assemble the original file.
"Tools -> Account Settings -> Offline & Disk Space -> Disk Space" has a setting to limit the maximum message size that you can download, to save disk space. Verify that its not enabled.
Another possibility is that the POP3 server is timing out. It defaults to 45 seconds. You can increase this to 180 seconds by setting mail.pop3_response_timeout to 180. The writeup on how to change settings explains how to do this as an example.