Does the radio signal decay when it travels through the intergalactic space?
All electromagnetic radiation from a point source - which a normal radio transmitter is - propagates according to the inverse square law which means that the intensity of the signal is inversely proportional to the square of the distance. This happens on earth and in deep space equally.

So this will mean that for any signal there will be a distance at which it's becomes indistinguishable from the background noise of the universe. However, that distance will depend on the initial strength of the signal.