I have had similar with video clip attachments sent by a camera. It most commonly happens if a message is moved from Inbox to another folder by a filter. Using Properties|Repair on the folder usually fixes it. Another workaround is to save the message as an eml file (say, on your desktop) and then open that eml file in Thunderbird. The attachment then correctly appears. Sometimes just forwarding the message (ideally to another account) gets you a working copy.

I know that in my case the attachment is there. I can see the binary content in source view. I can copy and save it as a text file, decode it from base-64 to text, save that as an avi file and then play the avi file. So the data is there.

I suspect it's a problem with the indexing in Thunderbird. Repairing the folder forces it to re-index, and saving it as eml detaches it from the indexing file. Forwarding causes it to be re-parsed and the attachment recognised for what it is.

In your case, the scanning by your AV may also be interfering with the handling of the message. Try turning off the real time scanning of email. Your runtime/on-demand scanner will still catch any bad content in attachments and so forth.