Most network infrastructure has at least a few hours backup on it. By the look of the equipment I see here and there I'd say they run for days without a working grid in a lot of places. Wired phone networks keep working if your modem is powered. The exchanges also have hard core power backup, usually diesel generators too.

Not a city block per se, but portions of my large neighborhood are out, yes.

I assume the internet provider’s equipment either isn’t affected or they have some backups of their own. Being low power though, the internet signal is still flowing. My modem and router were powered by UPS, and they assume the internet providers station remained online.