The capacitor and ballast may have specific temperature ratings, but most effects of temperature (ie. short of the electrolyte freezing solid) are gradual, and the point of cutoff chosen for the rating is fairly arbitrary
Together with additional factors - age of components, resistive condensate films forming (including on the tube), and other abnormal conditions, the actual non working range may end up within the rated range
For example :
Consider a ciruict where the small chip Vcc electrolytic is charging from the rectified line voltage through some high (in the Megs range) resistor. The current supplied by the resistor is not sufficient for the continuous operation of the chip
The chip has undervoltage with hysteresis. Once the cap charged to the high level of this hysteresis window, the chip starts using it, and there is enough energy in the cap, that the chip can start running the circuit before the cap discharges to the low level
What if the cap discharges so quickly (e.e due to capacity loss) or has so high voltage drop (due to ESR), that the chip never gets its starting voltage for long enough time to even generate the 1st output pulse. The circuit will appear dead, the power draw of the circuit will remain basically VRectifiedLine / Resistor
Measure whats up with the voltage on this cap. Evan if you dont have a scope, just DMM can give a general indication