I'm pretty sure it's because the particles are coming into existence and going out of existence at the same rate, so the net energy difference is 0.
But I'm not a physicist so I may be totally off.
You may Not be a physicist, but that actually is an excellent hypothesis. Upon entering existance there would be a total energy greater than beginning, upon leaving it would go back to equilibrium. And, it is to my knowledge that the two happen simultaneously. That way it wouldnt violate conservation of energy.
In reality, the situation is much more complicated. In the vacuum, you can have a particle-antiparticle pair (like, electron-positron) that is created and shortly thereafter annihilates. But before it does, the electron can emit and absorb a virtual photon. But before the photon is re-absorbed guess what, it can turn into an electron-positron pair. You can keep going with this, to higher order quantum loop corrections. You can go forever. And all orders in principle contribute to the energy. Fortunately, the amplitude decreases with continued higher loops, allowing perturbation theory to yield a convergent result.
And that result is what is called the VEV (vacuum energy expectation value), which is nonzero. The vacuum has a non-zero energy due to violation of energy conservation. It CAN be violated, nature just follows very specific rules about how it does so.