Note: I'm only talking about real photons, no virtual particles.
The argument that Griffiths gives, is (p79)
and although I have respect for Griffiths, I'm wondering if this isn't a fallacious argument: the photon might not have mass, but it has energy...
Another argument might be (I'm guessing): "the kinematics does not allow it", but I think that kinematically it would be allowed, for example, for a photon to decay into three new photons (with longer wavelength).
Yet another argument might be: "the concept of half-life is not well-defined for photons, since they have no reference frame where they stand still". That might be true, but that still doesn't explain why photons do not decay.
What do you think is a convincing reason for the impossibility of the decay of a single photon?