As an experimentalist, other similar null searches are the search for proton decay, the search for fractional charge, the search for electric-dipole-moments (of electrons, neutrons, atoms, etc.), tests of lorentz symmetry, tests of the unitarity of the CKM matrix, the search for Majorana neutrinos, etc.

The lack of proton decay is first on that list for a reason. Nobody really knows why protons are so stable.