While all of the recommendations given so far are very good, you did ask us to focus on narrow gauge, and most particularly, runs that are probably soon to disappear. While NONE of the trips recommended are really secure for years to come, some are more likely to be around then others. Based on this, I would recommend the following and why.
-See the White Pass & Yukon rotary open their line in the spring. Any rotary puts on a great show and to see a steam one is getting very, VERY rare. No guarantee that the WP&Y will continue to run their rotary in the future. See it while you can.
-IF, the C&TS ever run their rotary again, you MUST take the time to see, and hear it. It may already be too late to see this spectacular show but if the chance ever comes again. Don’t hesitate
-Back to the White Pass & Yukon, ride their steam train from Carcross to Lake Bennett. This run has been in the works for a while now and there is no guarantee that it will be a success. While I hope it is, this run will carry less passengers and cost more in steam maintenance then the southern end of the White Pass & Yukon out of Skagway. I hope the 69 and maybe the 73 will be making this run for years to come, but you never know.
-See and ride and hike the East Broad Top. This is a real, historical gem of narrow gauge history and despite the valiant efforts of the Friends of the EBT, this place is still in danger. The friends have a huge job trying to save what they can but somethings will fall through the cracks. See it while you can and consider supporting the Friends of the EBT.
-See and ride the 4-4-0 Eureka. It does not run very often and it’s owner Dan Markoff may someday decide that it’s not worth all the work and effort or the insurance cost to truck this beautiful engine to a railway and run her anymore. This is also the only chance you will have to see an engine of this era running. Don’t put off riding this engine and say “she will be at Durango again NEXT year. I’ll ride it then”. We used to say that about the N&W 611. Years from now when this engine is in the Nevada RR Museum, you will be glad that you took the time to see it working up a 2.5% grade heading to Rockwood.
So far, I have only talked about the stuff here in the States. The stuff in Central and South America should be on your list since much of that stuff only runs on a year to year bases.