I am a little unclear on what ramifications a negative quartic at high energies has on our world at low energies.
(1) First of all, is it that there is a second, isolated minimum that appears at higher energies, or is it just that the original minimum at $246$ GeV was modified under RG?
(2) Assuming its just a single minimum that was modified under RG: Now say the SM is correct at low energies with a 125 GeV higgs. Then we use RG to evolve up to some higher energies where the quartic is negative but the higgs potential is stabilized at some other (larger) field value by high-dimensional operators. Doesn't this new potential minimum just evolve back into the minimum at $v = 246$ GeV under RG evolution down to lower energies? I don't see why this is such a big deal, the vev shouldn't be RG invariant to begin with no?
Measured Higgs mass and vacuum stability and http://motls.blogspot.com/2012/07/why-125-gev-higgs-boson-isnt-quite.html?m=1 are related, but I don't think it addresses these particular questions (or at least in terms I understand).
EDIT: Just to clarify my confusion. According to Terning's 'Modern Supersymmetry' pgs 78-79 in the MSSM the higgs gets a negative mass squared, and hence a vev, radiatively using the initial condition that all the masses are positive at high energies. This means at high energies the higgs potential is stable, and at low energies its unstable. So if you run the MSSM at low energies back up to high energies it will look like you are expanding around the wrong vacuum as well? Isn't this the same thing as what is happening in the Standard Model?