Most plausible future liquid fuels will keep long term in sealed containers.
If your zombie apocalypse hits today - fuel stabilizers / reprocessing as already answered, however if it arrives in the near future, and the country it arrives in is phasing out fossil fuels, you may not need to worry about this.
There are potentially net-zero-carbon fuels that many latest gen petrol cars can already run on (or be modified easily to run on) including things like methanol and ethanol. These can be generated renewably from as little as water, co2, and energy, and if that energy is renewable you have a green fuel that's backwards compatible with existing car fleets.
If this fuel is available like current gasoline it will last a very long time in sealed containers. A sealed underground tank full of ethanol at a petrol station should last until the tank fractures. The fuel will marginally decay when exposed to air (it will absorb water from 100% until 95% ethanol), but there should be no problem sucking underground fuel tanks dry for years if they're airtight.