Probably either your startup circuit is missing, or
mis-calibrated.
Bandgaps without explicit startup will have -at least-
two stable DC solutions (there could be more, as the
feedback can flip from negative to positive at some
high current level, depending on device and circuit
details). But that's another problem for another time
as your issue seems to be between "off" and "closed
loop".
Many SPICEs leave a numerical "residue" which will
become the initial condition for the next iteration of
a loop (such as temperature sweeps). So if you have
a solution at -40C which shows "off", that "off" solution
is the first guess at (say) -20C solution, and if that
gets convergence, on to the next, and only a gross
numerical excursion or some change to device
characteristics (e.g. a strong roll-on of leakage or
subthreshold conduction) will break you out of that
"tradition".
Look to the startup circuit. A bandgap that pretends
to start without one, is just waiting to say "gotcha!"
at FOK wafer probe debug, or worse yet at low temp
final test with a PDA lot-reject limit.