5V promini powered with 3.3V is out of spec - Speed Grade diagram in the datasheet shows ~3.8V is needed for 16 MHz operation. None the less, folks do operate them that low and claim to see adequate operation.
On other hand, there was a '1284P thread yesterday where serial operations were not okay for a 3.3V powered part & 16 MHz - raising the power solved the serial issues.
I would use a normal diode with ~0.7V drop between the battery and NRF2401n+.
Try it with a resistor as a light load, simulating the NRF2401n+ current draw, see how it does.
Either that or get a switching regulator:
Or a really low LDO regulator that can take the 3.7V from a LiPo and make 3.3.