Currently there are 18 year old Yugos on the road, and dealers have been gone for over a decade now. If you can still find dealers willing to service an oldsmobile in 15 years from now, you'd have something to brag about. The problem is not finding parts - you can still get any part you'd ever need to keep a Yugo alive (the factory is still turning out cars, just not selling them here) the problem is just finding service. However, the Yugo is luckily a very easy car to work on, so for mechanically inclined owners finding a shop willing to work on Yugos isn't a big deal.
The Yugo will be around for a long time to come, because there are plenty of owners who are strongly devoted to their cars, and will do what it takes to keep them on the road.