I understand the purpose of the login is to keep nefarious people who 'obtain' your phone from knowing the whereabouts to your friends. Does anybody know how long the iPhone keeps the session open after you enter the password? Is it even user-configurable the time-out period?
just a guess: As in the App Store app a session is 15min, I would asume that a session in Find My Friends is also 15 min.
If you configured your phone to be locked (need to enter a pin after swipe to unlock), then you don't need to enter a password at all in find my friends [read somewhere, never tested myself].