There is certainly a large standard deviation on that 24 hour average. Some proteins might last a few days. But we are talking on the order of days vs. the disease which takes on the order of years to manifest. Anyway I assume that the disease manifests as a result of bad PrP accumulation (much like how tau and Abeta protein accumulation eventually results in Alzheimer's disease; in fact Abeta has been described as having "prion like" properties regarding how Abeta clusters beget more clusters). So as soon as you shut down PrP synthesis, I doubt CJD could manifest, even if the current PrP in your body was immortal.