Isn't it a meaningless question? Photons aren't things, but loosely localized areas of motion energy that's temporarily assumed the shape of a photon. Upon collision with other similar waves, it may change shape and become another partickey like an electron. But the light itself is a motion itself, which is a pure abstraction. At the end of the universe, photons probably will keep spreading over larger and larger areas, slowly turning into a uniform sea of that pure motion.
Yeah, this is like asking if energy has an infinite lifetime.
My suspicion that everything is made of pure abstract motion can be backed with a thought experiment. A spaceship with a light sail uses kinetic energy of photons that hit the sail. We know that anything can be dissolved into photons, we even know the exact amount of those photons from the e=mc2 formula, and when all those photons hit the light sail, they vanish from existence and become the kinetic energy of the spaceship. And what is kinetic energy? It's not even real. And as we know from the relativity theory, even as an abstraction, kinetic energy can't be measured with an absolute number, it has to be measured with respect to some imaginary reference frame.
The light also doesn't have an absolute energy though; like the ship's kinetic energy, the light’s frequency (hence energy) also depends on your relative speed.
None of this stuff is “real”, but boy does the bookkeeping seem to work out...