One of the most used features of Firefox on my computer is Firefox sync (previously Mozilla Weave).
However, once Firefox is upgraded from 3.x to 4.x (and now to 5.x), Mozilla Firefox stops syncing when Firefox is closed. The issue is default Privacy settings that shipped with Firefox and clears all history when Firefox is closed. This looks like a bug in Mozilla Firefox.
As a workaround to this issue, on Windows navigate to Tools –> Options –> Privacy Tab –> History and there set dropdown for “Firefox will:” to “Remember History”. For Linux, just navigate to Edit –> Preferences and follow same steps as above. These settings worked for me.
Hope it helps!