I have to agree with @Felix Goldberg. Communication wasn't the real problem. Remaining in power most certainly was, for many emperors. The mortality rate of emperors was as high as gladiators. Not that many died peacefully in bed. 

Communication was done with the [cursus publicus][1] which remained more or less in tact until the very end of the empire. That system had worked well when the empire was at its biggest height, so communication cannot be the real reason for its demise. 

What I notice is that both provinces and military units progressively become smaller over time. Part of that may well be to make better management possible, but a far more important reason is to make it more difficult to revolt. A governor controlling a large part of Gaul with 4 or more legions is far more dangerous to the emperor than a governor that governs a much smaller province, especially if the military command is separate. The governor would hold political power but not military power to make a bid for the purple, and the military commander didn't have the political power to support him. In both cases a lot less political and military power than in the past. 

Which, at least for a short time, solved another problem: more governorships and military commands to share out to adherents. In other words: the pie was sliced in thinner slices to satisfy more people. 

> How was communication in the Roman Empire set up

The *cursus publicus* was the Roman equivalent of the Pony Express. All throughout the empire were stations where riders and important travelers could change horses and riders. That way a message could reach Rome within about 10-15 days. 


  [1]: https://en.wikipedia.org/wiki/Cursus_publicus