This thing was driving me nuts: every time Mozilla Firebird (Windows version) opened a second window, next time I restarted the application it came up at the new window position instead of the position that I prefer. Earlier, I solved the same problem for Internet Explorer by making a certain entry in the Registry read-only. But Mozilla Firebird did not have a similar Registry entry.
Today I found the solution: Mozilla Firebird appears to store position information in a file named localstore.rdf, which is located deep inside your personalized Application Data folder (I suspect that the actual path may differ from one computer to the next). All I had to do was to make this file read-only (using attrib +r from the DOS command line) and presto: even if I move or resize its window, next time Mozilla Firebird starts, it starts using the old window position.