I don't imagine so. Take a look at Stanford's Orbis which is basically Google Maps for the Roman Empire. London to Rome was 27 days. Damascus to Rome was 24 days. That's under good conditions. Yet it held stable (more or less) for hundreds of years. From the late Republic until the fall of the West it lasted 500+ years. Even with periods of instability like the Crisis or the Third Century, that's a remarkable run.

Even in the smaller Byzantine empire exceeded 14 day travel times between important areas like Alexandria to Constantinople, which was 17 days in good conditions. And the Eastern Roman Empire lasted centuries more.

It should also be asked by what you mean when you say 14 days travel. Heroditous says that the Persian road from Susa to Sardis took 90 days. That's probably true for conventional travel, merchants, military forces, and the like. But Xenophon records a similar journey taking 45 days. So clearly really pushing can take a lot of time off the journey. That's also the route of the famed Royal Road, a route that had a Pony Express style courier system. We don't know how fast the pirradazish couriers could make the trip, but it was no doubt faster than Xenophon. But even a courier carried message would likely take more than 20 days to reach more distant provinces, and that's with switching couriers to let them rest. Plus Sardis was far from the most distant corner of the Achaemenid empire. Besides only the more important messages were delivered by courier. Routine reports and things like tax revenues used normal delivery services, taking months to get from the provinces to Susa (or Babylon depending on where the King of Kings was hanging out that season).

Empires large enough to take more than two weeks to go from center to periphery are rare. Empires that last longer than a few generations are rare. So states that are both large and long lasting are going to be doubly rare. So it may appear like a 14 day travel limit is some sort of natural law. But several states existed where communication from core to periphery could take longer, and in bad circumstances a lot longer.