Which of the following remains constant for a satellite in an elliptical orbit.

If the satellite doesn't have little rocket engines or other thrusters on it, AND it stays far enough from Earth that it doesn't have to plow through any air molecules, AND no pieces break off of it and drift away, AND there are no hamsters inside it running on treadmills connected to external thrusters, then there's no way for it to gain or lose energy, and its total energy remains constant.  

Some of its energy is always changing, either from potential to kinetic or from kinetic to potential, as its distance from Earth changes.  But the total stays constant.