The higher spaceship must travel at a higher speed than the lower ship since it has farther to go and, like the end of a pivoting line in a marching band, must go faster to keep up. Once both craft attain orbit about Earth, they go at constant speeds. So, at first glance, it seems like the higher ship need only to apply extra thrust when getting into orbit to attain the faster speed. But that's the rub. It can't attain faster speed at a higher orbit.
Orbital mechanics gets in the way.
The faster the orbital velocity for any object orbiting Earth, the lower the orbit, says John Hodges, British aerospace engineer. That's how Newton's laws of gravity and motion work out. The only way the higher spaceship can stay even with the lower one, is to continually apply power in the right direction. But, Ransom points out, the higher-orbit pilot won't actually fire his thrusters often if his orbit is only tens of feet higher than the other.