Resistor is not a good idea.
Current draw by nRF24L01+ module varies from
Emission mode current(peak): 115mA
Receive Mode Current(peak): 45mA
Power-down mode current: 4.2uA
http://imall.iteadstudio.com/im120606002.html
The Uno has a decent 3.3V regulator on it that's good for a couple hundred mA.
Are you sure it's not being shorted out by something and shutting itself down?