Does a photon have a minimum energy level, below which it disappears? As photons travel through expanding space they become red shifted, resulting in the CMB.
Eventually they will no longer be detectable as they continue to redshift.
Is there a point in the distant future where their energy level drops so low, its at or below some minimum quantum threshold and disappears?  Or does it exist forever with a steadily decreasing wavelength, never reaching 0?
 A: Lorentz invariance implies that a photon can have any amount of energy.
In particular, if a photon has the four-momentum $(E, E, 0, 0)$ (that is, it travels in the direction of the positive x-axis) then in another locally inertial reference frame that is travelling with velocity $v$ parallel to the x-axis with respect to the original frame, the photon's four-momentum is $\sqrt{(1-v)/(1+v)}(E, E, 0, 0)$, or in other words $E' = \sqrt{(1-v)/(1+v)}E$ where $E'$ is the energy in the new frame.
As $v$ approaches +1 (the speed of light in the positive x direction), $E'$ approaches 0; $E'$ can be made arbitrarily close to 0 by making $v$ sufficiently close to 1. As $v$ approaches -1, $E'$ approaches $+\infty$.
Thus we can see that if photons ceased to exist below a certain energy threshold $E_0$, Lorentz invariance implies that for every photon in the universe that exists, there is some locally inertial reference frame where it doesn't exist: it just has to be boosted enough so that $E'$ would fall below $E_0$. This is problematic because Lorentz transformations are invertible. If, in the other frame, there is no photon, it means there cannot be a photon in the original frame either, because a Lorentz transformation of vacuum results in vacuum.
If you stipulated that the law "photons cease existing below the threshold $E_0$" doesn't apply in frames that are sufficiently boosted as a way of avoiding the previously mentioned issue, then that would also be a Lorentz violation since it would mean the laws of physics are not the same in the original and boosted frames. If you said that the extremely boosted frames don't exist at all, then that would also be a Lorentz violation.
We can never, by experiment, completely rule out Lorentz violations, since there could always be Lorentz violations in the universe that are too small to detect with current technology. Thus, your scenario is not completely impossible. However, all searches for Lorentz violation have failed to find any, and imply that if there exists any such threshold energy $E_0$, it must be very, very small. See https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation
