Have you measured the current usage? The LM7805 is not terribly efficient and if you don't use the car regularly just the loss of the LM7805 and the on board regulator for 3.3v for the nrf2401+ can drain the battery. I did a quick LTSpice simulation and even with a super light load (100uA) the circuit will draw more then 5mA. And with a stock arduino pro mini it will be more like 7mA.
With a large battery It will probably never be an issue, but something like 3-5A drain a month is not nothing.
Maybe swap the LM7805 with a switching regulator. In any case make sure you remove /disconnect the led from the arduino that will save you 1.5 mA anyway.

Have the same problem with the stable branch as @Oliviakrk using the NRF24 transport on an Raspberry PI B, it might be a driver issue, is see that the make for the development branche builds the BCM drivers while the master branche does not.