Strictly speaking, falsification isn't really possible. For any piece of evidence that undermines a theory, it is always possible to add an auxiliary hypothesis to restore the theory. There is no logical point that requires the abandonment of any theory, and this is the case whether the thesis involves the supernatural or does not involve the supernatural.
“A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”
“Science advances one funeral at a time.” -also from Planck.