FOB-key not starting the car

I have a problem with my (new) Chrysler 300.
It was a minor annoyance when it started a couple of weeks ago, but now it is getting worse.
 
When I insert my FOB-key into the ignition switch, the car beeps, and the VSA light (the small red light just below the Fuel Gauge) flashed once, and then.... nothing. I turn the key into ignition, nothing happens, the panel remains off, no light, no sound.
Then I remove the key from the ignition switch, insert it again, and again until finally it works normally and the car starts. Initially I had to do that only once. Now it is 10 times or more before it comes back to normal.
I tried with my other FOB-key, same thing.
 
Do you have any idea what this could be?

take it to the dealer   I see the WINS modules go bad often on them.