It sounds like you are playing with multiple game windows open. Changing the setting in one window won't change it in windows that are already open.
And if you're changing the setting via 'Settings'/'Daily Chess' (as opposed to clicking on the icon on the actual game screen), are you remembering to press the 'save' button?
If none of that works, then i'm at a loss; better you than me, i guess.
Daily Chess: I set it on "Stay on current game" but, after I leave and come back, it changes to "Go to next game".
So I have to keep changing it back to "Stay on current game".
Can you put a button for "Stay on 'Stay on current game'"?
It used to happen rarely, now it's happening more and more frequently, twice today alone.