  It has been proposed that the observed diphoton excess at 750 GeV could be
explained within the constrained minimal supersymmetric standard model via
resonantly produced stop bound states. We reanalyze this scenario critically
and extend previous work to include the constraints from the stability of the
electroweak vacuum and from the decays of the stoponium into a pair of Higgs
bosons. It is shown that the interesting regions of parameter space with a
light stop and Higgs of the desired mass are ruled out by these constraints.
This conclusion is not affected by the presence of the bound states because the
binding energy is usually very small in the regions of parameter space which
can explain the Higgs mass. Thus, this also leads to strong constraints on the
diphoton production cross section which is in general too small.
