Don't get fooled with the specified data rate. Check if any errors (see Andy's reply) are being generated using a too high rate. Normally radiomodules follow what you put in, but sometimes it is good to settle for a 9600baud.
Check the /RX /TX pins if they work properly.
Put in an extra tantalium capacitor and a ceramic disc cap as close to the supply pins of the transceiver as you can get it.