not a facebook user for aloooong time now but when i did i always had issues with syncing and this might be your problem as well.
essentially i am not seeing a problem here unless.....
A) its running up your data charges because you think it is off and it is still on?
B) or it is keeping you logged on and you are missing IM conversations etc....?
but both cases are kinda a moot point as you said this only occurs when you are logging out......so essentially i dont see a problem, sorry i am not belittling your issue just merely pointing out that if the app closes and everything else works fine it might be something up with your local facebook server or a miriad of other causes but that essentially arent realllllyy affecting you....
see if you can reinstall the facebook app.. might help....:smileywink:
