The uncharged AdS4 soliton has been recently shown to be continuously connected to a magnetic, supersymmetric AdS4 soliton within N=8 gauged supergravity. By constructing the asymptotic superalgebra, we establish a positive energy theorem for the magnetic AdS4 solitons admitting well-defined asymptotic Killing spinors, antiperiodic on a contractible S1. We show that there exists only one discrete solution endowed with these boundary conditions satisfying the bound, the latter being saturated by the null energy supersymmetric configuration. Despite having negative energy, the uncharged AdS4 soliton does not contradict the positive energy theorem, as it does not admit well-defined asymptotic Killing spinors.