These nRF24L01 devices are tricky enough as it is, with multiple problem reports per week appearing in this forum, and usually insufficient power is the issue.
The modules which are described as nRF24L01+PA+LNA are usually worse in this respect.
Which model have you purchased ?
When the transmitter is not powered via the USB cable, how is it powered ?
The 200ms that I suggested came from the datasheet https://www.sparkfun.com/datasheets/Components/SMD/nRF24L01Pluss_Preliminary_Product_Specification_v1_0.pdf ch 6.1.1 where a 100ms following a power on reset is required. Some clones/fakes may behave differently.