Moon Jellyfish live up to a year on average in an enclosed, temperature controlled system, although with immaculate care they can live up to an additional year.
In the wild, the moon jellyfish lifecycle takes one year to complete. Juveniles are produced from polyps in the spring and adults grow throughout the summer. By the end of the summer male and female jellyfish mate and produce polyps, which grow and divide throughout the winter. The polyps start producing juveniles and the cycle repeats in the spring. This means the swimming medusa life stage of jellyfish is only around for a few months during the summer. Jellyfish have delicate tissue, so they are usually damaged by the end of summer and most of them die. In captivity, it's very unlikely for the jellyfish to reproduce, although it is possible, and the adult jellies live up to a year on average.
There is actually an "immortal" species of jellyfish that was only discovered a few years ago. It is the only animal known to be able to go backwards in its lifecycle and revert back to a larval stage.