Background
One usually claims that supersymmetry must be spontaneously broken. The reasoning is roughly the following:
Since $M^2=P^{\mu}P_{\mu}$ is a casimir operator of the supersymmetry algebra, all the particles in a supermultiplet will have the same mass. Therefore the electron and the selectron will have same mass, and we would be able to produce selectrons at the accelerators, which nowdays operate at an energy scale of $1 \ Tev >> m_e\approx 0.5 \ MeV$. But clearly no selectrons are ever seen at the $MeV$ scale.
The standard way to avoid this is to introduce some kind of supersymmetry breaking mechanism, of a similar kind of the Higgs mechanism in the standard model.
Question
Is it possible that susy is exact and not broken, but still supersymmetric particles can not produced in reaction of ordinary particles, basically because these reactions would violate the conservation of an extra (not yet known) quantum number?
Why is such a scenario discarded a priori, an so much effort is put into the study of the susy breaking mechanism?