Zener and forward diode tempcos can be made to cancel
(first order) but you have to beware things like high temp
zener leakage and low temp beta degradation as actors
that won't be noticed in a commercial temp range design,
but could make accuracy degradation accelerate further
from known territory.
I would not expect a dropout unless the BJT was operated
at a pretty low current density (then current starved times
degraded beta, might be on the wrong side of load-point).
Many commercial devices do not test for extreme-temp
attributes at all, and you might not be told just how much
scatter there is in the population, or how far out, in the
parameters that matter.