Hittade en "work-around":
It is a work-around, but it seems to work without altering the functionality of the software.
1) Open a new Firefox windows.
2) In the address line type: about:config
3) Click 'I´ll be careful, I promise!'
4) Type in the filter: places.frecency.updateIdleTime
5) Change the value from 6000 to 0
That should do the trick.
Basically Firefox is updating something every 6000 milliseconds, which obviously prevents the machine from sleeping. When you set it to 0, it doesn't update, whatever 'it' is. However, this doesn't seem to cause any unwanted effects.
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från: http://support.mozilla.com/tiki-view_forum_thread.php?locale=ca&forumId=1&comments_parentId=178042