Why should dark matter be stable (i.e., non-decaying)? People say that the dark matter has to be stable and electrically neutral. Since there is no particle in the Standard Model which is both stable (non-decaying) and electrically neutral it cannot describe dark matter. It is easy to understand why the dark matter should be be electrically neutral-because it doesn't have electromagnetic interaction.
But why should dark matter be stable (i.e., non-decaying)? 
 A: The main argument is that dark matter has been present for $13.8$ billion years. Dark matter makes up over $80\%$ of matter, and observations of the more distant regions of the universe appear to indicate much the same.
There are stable particles in the standard model. Weakly interacting chargeless particles in the standard model includes neutrinos that are stable. With the WIMP model it is assumed that dark matter is some form of weakly interacting matter. A supersymmetric candidate is the neutralino that is a condensate of the supersymmetric partners of the Photon, the W particle and the Higgs particle, called photino, wino and higgsino respectively, which have the same quantum numbers. 
The LUX ZEPLIN will make the most sensitive measurements to find WIMP forms of dark matter. If this does not detect any weak interactions from WIMP dark matter then it may be judged that dark matter is something other than WIMPs. The other possible candidate is the axion particle.
A: 
But why should dark matter be stable (i.e., non-decaying)?

Non decaying also means very large lifetimes, compatible with the age of the universe. It would be a very particular model which would have a particle which also decays only into neutral particles, neutrinos and/or photons. Charged decay products  with short lifetimes would be visible, not dark.
