Facebook web app keeps logging me off after just a short time? Any idea why this happens or how I can keep myself logged in?

You need to change your permissions, easiest way is to download and install the latest bossprefs, run it on your iphone and choose the more option on the top right of the app and choose the "fix user dir permissions" option. This fixed it for me.

yeah, it's a cookie issue, since cookies aren;t owned by root anymore but by mobile, facebook cant keep you logged in, i fixed it with a command line script i found after extensive web research.
Sry cant tell ya more.

Yeah the command line is

chmod -R 777 /private/var/mobile/Library/Cookies

need to use terminal in WinScp or Terminal on iphone to run the command, then alls good after a restart.

(Posted it incase anyone saw this post at the top and had same issue)

Yeah, what they said.

Basically, when Apple changed the user permissions, they forgot to set Safari's cookies properly. The only fix right now is if you jailbroke your device.