It certainly looks to me like some issue with power supply.
Have you added a capacitor close to the power pins of the radio?
It's also a good idea to power the radio directly from the power supply instead of through the arduino supply which is very limited.
@igpels - i use this code.
I would try a 47uF on the radio if you have 4,7 today to start with. To filter the output of the voltage regulator you add a 0,1uF and maybe a 10uF from VOut to ground.
