Not sure that it " senses" v drop-

Timer chip begins cycle @ ( threshold voltage achieved), closes NO relay after delay. Relay remains closed until voltage drops below threshold, @ which point it opens.

But if voltage never goes below threshold, relay remains closed, ballast remains powered, - no reset.

If yer getting brownouts, you could def be hitting points where voltage is low enough to break arc, but not low enough to release relay. Relay would seem to have failed.

But again, IANAEE.

Wish I could offer more than speculation.