I installed and cloud synced the android app. I set a passcode, and found that if I quit the app and then restart the app from a homescreen shortcut, or restart the app by holding the home icon until recent apps show and then select YNAB from there, the app doesn't request a password, but reopens where I left off. Rebooting the device resets this behavior, as does choosing manage apps and selecting "Force Stop". Once the app is opened again, and the password is re-entered, the app again opens without requesting a password, unless I choose the app icon from the apps menu. There should be a way to quit YNAB, that enforces the passcode. Maybe a popup that says "quit now?" when you switch to another screen, or a routine that automatically syncs and forces a stop.
Otherwise, great product.
Motorola Droid Razor,
Android Version 4.04
Let me know if you need any other information.