Can quantum Rabi model with A^2-term avoid no-go theorem for spontaneous SUSY breaking?

The hierarchy problem asks why the mass of the Higgs particle is so much lighter than the Planck-scale mass. Considering the interaction of the Higgs particle and an elementary particle in the Planck-scale, to cope with that big difference, the conventional calculation needs the help of an arbitrary, excessive fine-tuning, that is, the huge cancellation between the bare mass term and the quantum correction, without obeying a physical principle such as symmetry. Thus, it is often said to be unnatural. On the other hand, the theory of supersymmetry (SUSY) is a strong candidate naturally to solve the hierarchy problem. However, any sign of SUSY even for the quantum mechanics (QM) version had not been firmly, directly observed in the physical reality until Cai et al. reported the observation of N=2 SUSY and its spontaneous breaking in a trapped ion quantum simulator for the prototype model for SUSY QM. In this discussion, I derive a no-go theorem for the spontaneous SUSY breaking in the strong coupling limit for the quantum Rabi model with the A^2-term, and at the same time, I show another limit proposed in the scheme by Cai et al. can avoid the no-go theorem and take that model from the N=2 SUSY to its spontaneous breaking. I propose a theoretical method to observe how the effect of A^2-term appears in the spontaneous SUSY breaking.