The switched live you´re using is controlled by the BSI which stays active for a while after the ignition is switched off.
IIRC you use the orange wire on the Berlingo plug, which is for accessories, as your switched live. This will go on and off with the ignition.
I had exactly the same problem myself - now sorted.
How much is the fish?
I have a sub but I also have a removable face plate for my stereo and an off button do I use either of the two, normally removing the face plate so my sub turns off anyway and I take no notice of it being on but if I was to sit with the engine off and face plate on it does stay on for a little while like knobbly said it's the bsi.
I'd guess when unlocking the car the bsi becomes active then it turns the stereo on
53 plate Berlingo Multispace Forte 1.9D Polar White
wire the stitched live (normally red) to the drivers electric window live supply.
that will make it come on and off with the ignition
wire the yellow ( perminant live) to the battery.
now it will keep all the stations