Space in our universe has a vacuum energy and our expanding (actually, accelerating) universe is in fact gaining "dark" energy.
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.
https://ptolemy.berkeley.edu/eecs20/week9/timeinvariance.htm....
Time invariance is mathematical fiction. Haha. What a wonderful quote.
If this seems to violate the law of energy conservation, you're spot on. It is indeed being violated.
This is not fundamentally problematic by itself, because the law of conservation of energy depends on time invariance. Which doesn't hold in the case of an expanding universe. But it is an unsatisfying copout, and we hope that it can be resolved by the quantum gravity.