I’ve not had this problem myself it all goes to sleep once I open the drivers door. Does it respond to the power button next to the display? Does the dash board go dark when you open the drivers door?
Having asked the questions it still sounds like a fault. I’ve read on the forum recently of someone forcing a hard reset of the R-link system by disconnecting the positive lead from the 12 volt battery for a short while. The down side appears to be that the sat-nav will loose its stored data. It might be worth giving it a go, alternatively take the car back to Renault as it’s still under warranty. You might be able to do the same thing by pulling a fuse out but I’ve not seen anything that tells you which fuse is which, it might be a question for Renault. It shouldn’t be a secret.
Yes it does sound like a fault and may be draining your 12v battery. My car dash camera is hard wired to the car. It is activated and deactivated with the car. When the car wakes up so does my car dash and after a few mins of the car locking …the camera goes to sleep. That is what is supposed to happen. It sounds as though your radio is still obtaining power from somewhere.
It probably worth giving Renault a call about it. The radio has potential to flatten your 12 volt battery and cause you all sorts of problems. It sounds like the radio and R-link units aren’t talking correctly.