How long will the gas grid keep working without electricity? Sure, the pressure is likely maintained from a reservoir, but many of the control systems likely depend on electricity, and I could imagine some being fail-safe (solenoids holding valves open and shutting if power fails).

For a very long time. The natural gas infrastructure uses natural gas generators to run the pumps that pressurize the lines and the meters are 100% mechanical. There's no reliance on the electrical grid. I lived through Northeast Blackout of 2003 (visible from space, the extent was so great) and Hurricane Sandy (power was out for a week) and in neither case was there an interruption to natural gas service. In my 40+ years, I don't ever recall the natural gas service ever going "out".

Gas runs forever without electricity. My folks have a gas generator on a pad at their home because ice storms take down the electric grid every year in their town. This year it ran for ten days straight.

Pressure in natural gas infrastructure is maintained by pumping stations that are fueled by the gas. These are huge and impressive and usually located far from any town.

It depends how well it is maintained, like most infrastructure.

https://www.wvpublic.org/news/2014-03-10/ntsb-determines-cau...

They deliberately do not use grid electricity, as they don't like sparking and there is no need for it. It's just simple mechanical pressure regulators, along with gas turbine compressors on long supply lines to boost the pressure.

Have they ever used those pressure-reducing stations to produce electricity?

Never sure if it went from theoretical to actual.

https://www.google.com/search?q=natural+gas+pressure+reducer...