Frank, I don't think Firefox is completely closing when you close it out. If you are familiar, do a ctrl+alt+delete and look at the processes to see if FF is still running after you close the window.
Either way, make sure you're on the latest version.
Also, you can backup your bookmarks every once in a while by going to Bookmarks->Manage Bookmarks->File->Export.
I actually have an extension loaded up that exports my bookmarks to a file on the internet via FTP. This way I can synchronize my bookmarks between 3 different computers.
I've used FF for a long time now. It's the first browser that I was happy to leave Internet Explorer for. Much more secure and of course you can download all the goodies (extensions) from their website to further customize it for your needs.
+1 for FF