Probably the best example of that is the Holy Grail of wargames, Up Front! This card came has a well-deserved reputation for being an excellent game (although with tough rules) and it can be hard to come by in good condition without paying a lot. And it's becoming pretty likely that it will never again reappear, at least not in its current form. Even tougher to find are its expansions.
Another classic and beloved old Avalon Hill game that will never be reprinted in the same form is Dune. I also have the expansions for that game. This is one of the best multiplayer games out there, as well as one of the best realizations of a novel in game form.
In the case of Up Front!, the original artwork has been lost. So even though Multi-man Publishing has the rights (at last report) for a reprint, a new edition will require the same work as a new game. That project appears to have stalled however, so it seems likely that all the copies of Up Front that will ever be have are already out there.
For Dune there are plans for a reprint by Fantasy Flight Games, but it will have to be rethemed because FFG got the rights to the game system, but not the Dune license. Reportedly the theme will be set in FFG's Twilight Imperium universe. This may work just fine, but it will by definition NOT be Dune.
Ambush! is another system that I got in on the ground floor when it first came out. While copies of Ambush! are still available on eBay for reasonable prices, the expansions can be hard to find cheaply. This is a problem because, as a solitaire game, you need fresh missions for replayability.
I wasn't thinking about the long-term availability of those game system back in the day, but I do consider that now when making purchases. For example, I made certain to pick up an extra copy of Simmons Games' Bonaparte at Marengo because I suspected it would become a hard-to-find game. Simmons has since confirmed that there will be no reprint for that game.
The kind of game that's most likely to become rare are unusual designs from small publishers or those dependent on a license, as well as expansions. If you really like a game it seems worthwhile to make the effort to keep up with a series in near real time, because there is no guarantee you'll be able to get it later.