You should get one hour from the press of the button as you say..... if the battery is detected to drop off the radio gets turned off prior to the hour I believe... a sort of failsafe to draining your battery too far to effect starting.
I don't know, but I'm guessing that the battery is already at the point where playing it without the engine on will cause the voltage to drop too low. Just a guess!
If your battery is original then it is almost certainly on its last legs being 2012. I would get a decent brand in there... don't go for a Ford silver calcium!
They are woeful. Any reputable make from euro carparts or even Halfords will be cheaper and most importantly better.