I think it would depend on how sensitive your equipment is to power fluctuations. An uninterruptible power supply (UPS) would probably mitigate any effect that flickering power might be having on your service.
If you notice your electricity flickering and dimming, you're lucky to be communicating at all. The inconsistent levels may not be enough to reboot your equipment but if your modem is receiving reduced power, one could assume the strength of your upload signal is also reduced. Capacitors are suppose to "fill the gaps" but if the dimming outpaces its charge, you'd get weak power.
A UPS could bridge your levels but how widespread is this problem...at your neighborhood node, headend at Cox, Edge routers?