Czuch: Well, i am going through the Thunderbird: FAQs now for you, but i do not think anyone has had this problem by the looks of it. Most just export the file to Desktop (or wherever) then upload it to an on-line storage site or save it do disk.
My only other suggestion is to write to Mozy and see what they say, after all they must know where it would of been up loaded to and stored under. My only concern is did they bother with the address book ?