Your question is apparently based on the false premise that "Firefox deletes old bookmarks". This is a false premise because, out of the box, Firefox does not, routinely, do this. Your question ought to have been, "Why are my older bookmarks no longer accessible in Firefox?"
Anyway, see this Mozilla KB article and see if anything there helps. It could be that the Firefox bookmarks sync server accidentally lost some of your bookmarks due to unintentional data loss, and then proceeded to sync those changes to each computer. It's hard to say for certain what happened. But it is definitely not because Firefox is programmed to delete old bookmarks for no reason.
With that said, some third-party Firefox extensions may have enough permissions to do this. So I can't rule out the possibility that there exists some extension out there that will delete old bookmarks. I don't know what such an extension would be called, though.