The problem is not loss of capacitance, it's leakage.
Leakage will prevent the capacitor from charging to its full voltage.
The neon indicator is a voltage comparator circuit. It comes on when the voltage across the capacitor rises above 250 volts (for example).
If the voltage can only rise to 240 volts, the neon indicator will never light, but the flash may still fire at reduced brightness.
This is the way flash systems work. I was a warranty repair station for Novatron strobes, so I'm reasonably familiar with the technology.