The issue is likely due to multipath interference. This happens when a combination of the incident signal, and the same signal reflected from a nearby object out of phase, arrive at the receiving antenna. This causes localized signal fading when the signal arrives about 180 degrees out of phase, but also depending on the modulation/coding scheme used can also cause difficulties in decoding the received data.
It's for this reason that many modern devices, such as WiFi and cellular, incorporate multiple antennas to create diversity, as well as modulation and coding schemes that are more tolerant to this phenomenon.
You could switch to a directional antenna which would improve thing however since your antenna is on a moving object that is not practical. Does your quarter-wavelength antenna have an appropriate ground plane? The lack of a suitable ground plane can hurt the performance and result in rather unpredictable radioation pattern (in other words, your omnidirectional antenna can end up having undesired directionality!). An effective antenna can be made simply by folding back the shield of coax over itself the right amount, and using the center conductor as the radiating element. This creates a dipole antenna of sorts. Lastly, if you have this radio module on your own PCB do make sure you have properly designed impedance-controlled traces from the module to the antenna.
If none of this helps you may have to look at a different radio transceiver, perhaps one more suitable for use on a radio controlled vehicle.