Actually, the Milky Way may have died at least once around 7 billion years ago; it revived after a period of 2 billion years, during which a whole bunch of stars died, going supernova and ejecting their outer envelopes into space, filling the galaxy with material for making new stars.
The Milky Way currently has a relatively slow star formation rate, around 1 to 2 solar masses per year, but it's also not hurting for new material.
Our galaxy is a cannibal, with a history of absorbing other galaxies and all their wonderful star-forming material over its 13.5 billion-year lifespan, and it's far from done.