Are you using any encoding such as Manchester to enocde your data ?
These RF modules are not very powerfull and most of the time they do not include encoding in hardware so you'll have to do it yourself.This encoding-less makes them vulnerable by the noise.whenever you're transmitting data because the transmitter power is more than noise you don't get too much noise in reciever (depends on the distance between the transmitter and reciever).but when nothing is being transmited by the transmitter Receiver is more vulnerable by the noise.(Due to the Automatic Gain )

Farshid