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I'm going to start this off with the Monster Hunter Rise demo, which is only available for a limited time, and which SO MANY PEOPLE WANTED that them flooding on to get it crashed the eshop. The demo will be available up until January 31st, so it's not a tiny window, but apparently the desire was huge. The game itself may need to have its own thread, but I don't think the announcement of the demo does.
I don't give a hoot about Monster Hunter, but I know it's pretty popular, including with several people here on FOGU. If you're interested in that demo, don't fail to grab it by the 31st.

I really despise this trend, though, of Nintendo putting out things with limited time availability, since I believe it's to manufacture scarcity value, or capitalize off of FOMO, which is a dirty trick, imo.