One more significant factor to add to the already good answers here:
We think of bureaucracy as a bad thing because it means a lot of red tape and boring stuff we don't want to deal with, but in history, it is the invention of bureaucracy that allowed for the development of very large empires. The Chinese did it very well quite early, with a class of people dedicated to be civil servants by a government-oriented religion that reinforced the authority of the Emperor with "submission to authority" ideology. They were able to maintain a very large and very stable empire for a very long time.
Bureaucratic technology was key to ancient Rome's success, and in fact is likely a major reason Rome was able to maintain a large empire after the Greeks had failed to keep Alexander's empire (or it's parts) together. Romans were very good at standardizing things like measurements, communication protocols, weights, even the layout of towns. It wasn't just their extraordinary road system that facilitated communication and commerce, but a very carefully organized system of civil servants and delegated authority to local governors and cities, all meshing together in a bureaucratic apparatus.
After the end of the middle ages, technology had made armor outdated, but it took warfare a while to transform. Napoleon really forced the world to adapt to the new technological paradigm, but he did it not so much through his knack for tactics on the battlefield as much as his radical use of bureaucratic machinery to create the modern nation state. Napoleon realized that since muskets were cheap and simple to learn, and very hard to defend against, the new paradigm of warfare wasn't "who has the best army?" but "who can replace their expendable army the fastest?". He weaponized the huge mobs of starving French peasants by drafting them, throwing together massive armies faster than his enemies could organize. To do this, he turned France itself into a massive machine for churning out badly trained cannon fodder. That is where everything from the modern census to public education comes from: the Napoleonic paradigm of warfare seen most clearly in World War I. By the 20th century, bureaucracy was the most important weapon of war on the planet. WWII was won entirely on that basis.
So my three factors I would say are ABSOLUTELY critical to determining the possible expansion of an empire are:
- Speed of communication, as mentioned previously.
- Dependability of travel, again, as mentioned.
- Sophistication of bureaucratic systems.
The largest land empire in history was that of the Mongols, and it hinged entirely on the organized nature of the governing body, which was capable of coordinating effort across thousands of miles of territory. Loyalty of state agents, incorruptibility of functionaries, reliability of emissaries of the Imperium are all units of measurement for how well bureaucracy functions. In a case where travel requires years of time to cross vast distances in space, you need systems in place to ensure the long term loyalty of representatives of the state as well as the incorruptibility of your communications.
It is worth noting that the more efficient your bureaucratic apparatus, the more resistant to change your society becomes. This is because the entire point of bureaucracy is to guarantee rigid loyalty to the original intent of the central authorities. It has a natural dampening effect on innovation, change, and adaptation. This is why Rome declined, why China had multiple crises, periods of chaos, and eventually stagnated technologically until it was WAY behind the rest of the world, and why the USSR fell apart. The more territory you can control from one central point with one small group of people, the less room for independent thinking there is for everyone else. That's how you get left behind by the innovative, creative "barbarians" outside the imperium.