On Earth, storms can last a few days. The Great Red Spot on Jupiter is a storm that has been going on for more than 400 years now. What is different on Jupiter that makes it possible for storms to last so long?
Standard answers, as found here, (partial quote)
Unlike Jupiter, the Earth has land masses that cause major storms to lose energy due to friction with a solid surface. Without this feature, Jupiter’s storms are more long-lasting. However, the Great Red Spot is long-lived, even by Jupiter standards. Researchers don’t quite understand why, but we do know that Jupiter’s storms that are located in cloud bands with the same direction of rotation tend to be longer lasting.
So, we know some of the probable reasons, and don't know the full story yet. Keep in mind that the current RedSpot might be a 3-sigma event, even for Jupiter.