No, it is not, your premise is false (in our real world. TM.) but your reasoning is good.

Energy does not vanish, you need a process to remove energy of a system.

Think in the planets orbiting the sun or the energy contained in a damm with millions liters of water. The energy is not dissipating itself, it is constant, forever.

So as long as the system is not disturbed, keeping the system in the same state is energy free because you only need energy to alter the system. Even of the energy distributions is not evenly balanced through it.

Disclaimer about the real world