Question

How might've geography made it hard for Japan to keep control of its empire?

Answer 1

If it is considered during the period of WWII I would say because the empire covered a huge extension, mainly in the Pacific, consisting of islands and atolls very far from each other and from the metropolitan territory.

Explanation:

Observing a map of the area covered by the conquests of Japan in 1942 we can se the enormous extension of the empire:

This extension and the geographic characteristic of being formed by islands separated by vast extension of sea made the empire very difficult to control and defend.
The Japanese army couldn't possibly hold every island at the same time at least in the Pacific area!