In this article we analyze the radiation loss from a high energy cosmic ray
proton propagating in a spacetime with non-systematic Lorentz violation. From
an effective field theory perspective we illuminate flaws in previous attempts
that use threshold approaches to analyze this problem. We argue that in general
such approaches are of rather limited use when dealing with non-systematic
Lorentz violating scenarios. The main issues we raise are a) the limited
applicability of threshold energy conservation rules when translation
invariance is broken and b) the large amounts of proton particle production due
to the time dependence of the fluctuations. Ignoring particle production, we
derive a constraint on the magnitude of velocity fluctuation $|v_f|<10^{-6.5}$,
much weaker than has been previously argued. However, we show that in fact
particle production makes any such constraint completely unreliable.
