[titzer]

Space in our universe has a vacuum energy and our expanding (actually, accelerating) universe is in fact gaining "dark" energy.

https://en.wikipedia.org/wiki/Dark_energy

[cyberax]

There is no known mechanism by which the lost energy can drive the expansion.

Moreover, expansion without dark energy would still cause the kinetic energy loss.

There are attempts to define the total energy of the universe in GR in such a way that it is preserved, but so far none are really successful.