Which version of FlashFXP are you using?
Older version of FlashFXP are unable to use LiveUpdate as they point to a location that no longer exists.
You will need to manually download the latest release from our website
http://www.flashfxp.com/download.php
You may want to backup your current FlashFXP installation or install FlashFXP into a new folder, just in case you run into complications.