A short life, and a very long wait
Ask "how long does a brine shrimp live?" and the honest answer depends entirely on which part of its life you mean. As a swimming adult, its life is brief. As a dry, dormant cyst, it can wait out conditions for longer than most pets are owned.
Weeks to a few months as an adult
Once a brine shrimp reaches adulthood, its remaining lifespan is modest and highly dependent on conditions.
A few weeks to several months
Water temperature, salinity, oxygen levels, and food supply all push adult lifespan up or down. Under favorable conditions a female can produce roughly ten or more broods across her life; harsher conditions shorten everything.
Around 2–3 months
Home cultures and novelty kits — including Sea-Monkeys — commonly report an adult lifespan in the two-to-three-month range, longer with a stable temperature around 70–78°F (21–26°C).
Suspended animation, for real
A dried brine shrimp cyst enters a state called cryptobiosis — its metabolism drops so low it's effectively undetectable. In that state, it isn't really "alive" by most working definitions, but it isn't dead either: add water, and development resumes as if no time had passed.
Kept dry, dark, and free of oxygen, brine shrimp cysts have been reported to remain viable for decades — commonly cited figures run to 25 years or more, with some estimates going considerably higher under ideal storage. It's the same trick that let a 1957 novelty-pet marketer sell "instant life" from a paper envelope that had been sitting in a warehouse.