The rule seems too simplistic. What's so special about 1 month? Is the significant value time to communicate, time to move military forces, or something else?
For instance, for your hypothetical interplanetary empire: How could a capital, with a military that can move at 1% light speed, effectively rule over a colony one light month away if the worst it could do for ten years is send a nasty letters over radio? Having local forces isn't a good answer, because one of the easier paths to rebellion is for the leader(s) those forces to declare independence and make themselves kings.