To stay logged into your site in Photon for Android,
1. Press the Lightning Bolt button to enter Flash Mode (BEFORE logging in)
2. Log into your Site. Check the 'Keep me logged in box'
3. Open and run your game/application
4. Exit the browser as wait for a minute (to make sure your flash session has ended)
Open the Photon browser again and press the lightning bolt to get into flash mode. You should be logged in as normal.
Please also make sure that Gear Icon -> Private Browsing is off.