They haven't died out, a third of Mongols today still maintain a nomadic lifestyle and similarly there are still nomads across the Eurasian steppe. As for why their military significance declined..

Population wise, the Mongols and other steppe factions always faced the problem of being outnumbered by their rivals. This only got worse over time as better agricultural practices and technology improved and helped populations grow. Funnily enough, the Mongols played a large part in doing this by sharing technology from all reaches of their empire together and kickstarting use of the printing press which made distributing knowledge easier. Meanwhile there's only so many cows/sheep/goats you can raise with so much grass to support so many people, the pastoral life is a simple one and didn't improve like the agrarian life did.

Military tech wise they were outpaced too. On the strategic scale, trains made the horse obsolete for long distance travel and on the tactical scale the mobility horses granted wasn't all that important when everyone was fielding guns and cannon.