It is difficult to assess how much communication issues affected the decline of Rome. On the one hand, during the period of barbarian invasions, the time involved in repositioning legions may have contributed to losses in individual battles, but on the other hand, since the communications networks in the fourth and fifth centuries were just as good as the ones in the first and second centuries, when the empire was thriving, it is difficult to say that this was a significant factor, except perhaps in the case of Roman Britain, which was at the end of a very long communication line. Rome had excellent road networks and postal service, with fast horses and messengers stationed at regular intervals along the roads. More important in the decline of Rome were the barbarian invasions, lack of clear imperial succession (resulting in many civil wars), and eastward shift of the center of power.
Also, when thinking about the "fall" of Rome, it should be noted that the eastern Roman or Byzantine Empire persisted until the 16th century, and so it might be best to think not so much of a "fall" as an eastward shift and gradual abandonment of the west.