The usual circuit (found widely across the internet) for a true random number generator's (TRNG) entropy source is a reverse biased transistor like so:
Q1 is typically a 2N3904 as it has been found to be quite noisy the wrong way round running in breakdown mode. +ve is typically in the order of 11V. This topology works well initially.
I came across someone who had built a TRNG and experienced problems whereby "after about 3 months of use the noise signal would drift." I've seen other references to long term degradation of such a topology but can't seem to locate them at present.
I have the sense that continuously shoving electrons the wrong way up a transistor might be detrimental, but have not found any references to prove this one way or another. After all, this is not the principal use case for a transistor.
Could the junction suffer gradual and irreversible damage thereby altering it's noise characteristics? Zener diodes are another situation altogether as breaking down is their modus operandi.
Three references on E.SE discuss reverse biasing, but not long term stability:
Is a reverse biased transistor stable in the long term?