The Mega just don't supply enough juice for the NRF24 module on the 3,3volt output pin.
The arduino.cc info for the MEGA2650 says:
3V3. A 3.3 volt supply generated by the on-board regulator. Maximum current draw is 50 mA.
I think the problem is the nRF24L01 transceivers take a short current draw during transmit. IF you add a 10uf to 100uf capacitor in parallel with a .1uf capacitor across the radio module's GND and 3.3V pins it will probably work.
The data sheet for the nRF24L01 HERE: shows the supply current being less than 15 ma. But that's an AVERAGE.
I'll do some MEGA tests soon.
I added 1.0 uf tantalum capacitors on two radios that had sometimes been flakey and they are 100% solid tonight.