The Summer Asian Games are held every four years, but the Winter Games is not. It was held 1986, 1990, 1996, 1999, 2003, 2007, 2011 and 2017. Is there any specific reason for this?
As you listed, it was held from 1999 to 2011. But the next Games after 2011 was held in 2017 which is one year before the PyeongChang Winter Olympic Games. It would gather more attention about winter sports.
After 2017 Games, there was no city that would want to hold the Winter Asian Games due to financial reasons.
Recently, Trojena, a city being built in Saudi Arabia is selected to be a host city for the 2029 Winter Asian Games.