Premium gasoline or premium gas does not last any longer than regular gasoline.
Just like regular gasoline the premium gasoline has the same storage life of around 3 months before the gas goes bad from sitting.
All gasoline no matter what type will go bad and lose it's octane and not be able to run in a car or other vehicle after around 3 to 4 months.
But when you do use premium gas your cars engines does tend to have more power and runs a bit better and some cars do get about 1 mile per gallon better in fuel mileage.
So in that case premium gas could last a bit longer because you can go a bit further on premium gasoline.
But the premium gasoline costs a bit more than regular gas so you're not really saving any money by buying premium gasoline instead of regular gasoline.