Hands Free Keycard – no longer works properly

Hello forum community, today I wanted to drive my wife’s Scenic (BJ 2011, equipment Bose) with the second key (which I used the last time about 2 months ago). But unfortunately the doors remained closed. An immediate battery change did not help (the 3V battery shows in the measuring device 3.2 V, is therefore full)… Our Scenic has the system, in which you can always leave the key in the handbag/hose. You do not need it to open/close the doors and also not to open the door. Starting the engine. I opened the car with the “first key”. Then put it out of reach of the car and started the engine with the second key (key before put in the shaft). The engine has started. Now my question: what could this be? Hopefully the key does not have to be coded (engine goes on). Or? Since June the car is unfortunately out of warranty… Thank you already in advance for your help.