Energy is always conserved, because that's the definition of energy. When an experiment discovers that energy is not conserved, that means we've discovered a new kind of energy (kinetic energy, gravitational potential energy, electrical energy, etc). This is semantics, not physics.

The only way to disprove conservation of energy would be to show that measurable energy -- in _all_ forms combined, varies in quantity in unpredictable ways. And it would be hard to differentiate "non-conservation of energy" from "dark energy" we can't measure with current tools.