The power consumption of the NRF comes in spikes, which will cause voltage drop.
As the batteries are used, you see lower output voltage under load - so those spikes result in the voltage drooping. The two bigger caps would be better able to counter this, since it transmits very quickly, and then the load is mostly removed, and the battery voltage recovers and the caps recharge - so the batteries can get more-dead before the device stops working. That'd be my guess, at least.