There is such a thing, called "stability bound" on mass of the Higgs boson. The basic idea (as I understand it) is that we take Higgs self-coupling, and calculate its renormalization running. And it turns out that for certain initial conditions, it becomes negative at some higher scales. So the Higgs potential becomes unstable.
The initial value for running self-coupling is uniquely determined by the Higgs mass in the Standard Model (SM). And for the $m_h=125\,GeV$, we are actually in the "meta-stable" region. Meaning that the coupling, indeed, becomes negative, but the tunneling time through the "potential barrier" is larger than the lifetime of the Universe. Here is the plot from a recent review on the topic, http://arxiv.org/abs/1112.3022:
Red dashed lines denote scales at which self-coupling become negative. How can sense be made of the whole construction?
We need a stable vacuum for consistency. How can we start with a consistent model at lower scales and arrive at an inconsistent model at higher scales? Does it mean that we can start with inconsistent models at high scales? Doesn't the whole thing contradicts itself from the very beginning?
Is there a basic logically consistent and logically thorough description of all that "stability" argument?