Actually safer to stay logged in i think, less chance a logger will catch your tkc password, and if your dumb like im sure alot of the people are online its the same password to log into your hotmail account, where they can report a lost password on your paypal account since you have your account hooked up to paypal they can make purchases.
by no means is this a tutorial on how to "hack" into paypal.
its for educational purposes only
and if you stay logged in then the worst that can happen is they can steal your cookie so they can alter it to stay logged in on their computer.