Technically the last vestiges of the Mongol Empire didn't get conquered or otherwise fall until 1705. Given that's a 500-year reign, I'd say that's pretty good. The Yarkent Khanate was the last bit of the Mongol Empire, ruled by a descendant of Ghenghis Khan, and not subject to another state. It was conquered by the Dzungars in 1705.
As to Alexander, yeah his empire broke up into Diadochi states on his death, but the last of the successor kingdoms, the ones founded in the wake of Alexander's death, was the Greco-Bactrian Kingdom in Central Asia, and it lasted until 10 AD, that's 335 years.
There are some Empires that didn't last nearly that long, so saying that they didn't last in one form or another is a bit of a misnomer