Asiana's points expire on a rolling basis. For Diamond members, I believe that would be 12 years after the end of the flight for which they were awarded, perhaps 10 years for regular members (I don't remember off the top of my head).

Your activity only affects status qualification. I actually quite like this system, as it doesn't lead to all of your miles expiring at once if you spread out your flights (I donated my Air France miles to charity to have them escape this fate)

Anyway, the take-away is that as the others mentioned, you'd best find a way to use those miles.