Die attach with some glue / conductive epoxy could have an effect. With a glue the glass temperature may be considerably lower than for the epoxy in the FR4 material (something like 150 C). I rememeber a 2 K epoxy I used with a glass temperature of 100-120 C. After heating close to the glass temperature the rate off cooling can have an effect on the properties. A glass temperaure close to 50 C would still be unusually low, but may be possible for an intendionally softer glue.
In theory the heating to 50 C could have an effect that lasts longer than 1 day. So with a dayly heating cylce one may not see mach change, but letting it sit cold for 9 days may be enough to accumulate. In this case one would still have some daily effect, but it may not be obvious in the noise. Averaging the data from the same time from different days may make such small effects from a daily cycle visible.
With a zener based reference, there could also be some electronic memory: hot electrons may cause all kinds of strange excitations, like the low level light emitted from some zener diodes. In theory the burried zener should at least keep the hot electrons away from the surface, but some of the burried zeners still show the glow. Some electronic states, especially in the oxide can have a rather long lifetime. Excitations from radioactive decay are known to accumulate over thousands of years and can be used to date some ceramics.
The effect of the power outage could be the missing heating cycles, but it could also be just the time the zener was not active and thus no longer exciting long lived state and this way reduce the number of such excited long lived states.
A related effect may be charge accumulation on the oxide surface of the chip. The oxide is a very good isolator, but still not perfect. Just normal lateral electric field could cause such charges to slowly build up when in operation.
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