The issue is that, while the question is valid, you're ignoring half the system. Let us assume that there are 100 units of energy in your system. Here are the various types of energy and their starting values:
Potential Energy (rocket fuel) - 100
Kinetic Energy 1 (spaceship motion) - 0
Kinetic Energy 2 (any other object motion) - 0
Thermal Energy (heat) - 0
Light Energy - 0
Taking the first letter from each energy type (simplified I know) we come to the equation P+K1+K2+T+L=N (net energy) = 100
After your first burn you've converted some of that potential energy to the other forms. Thus you end up with P=80, K1=9, K2=9, T=1, L=1. Net energy remains at 100. What is important to note is that the kinetic energy is evenly split between the spaceship and the exhausted particles that created the thrust. You do a second burn, dropping K1 to zero. However to do that you increase K2. Note that the new particles coming out are moving faster because they have the added velocity of the spaceship. Since the spaceship was lighter due to less fuel you consumed less potential energy in the process. Thus your new numbers are P=62, K1=0, K2=34, T=2, L=2. Your K2 increase is due to its original energy, the energy from the new burn, and the energy imparted on it by the ship movement.
This is all, of course, drastically overly simplified but I don't feel like dusting off my old textbooks.