Simply put, they didn't. There are millions of Maya alive today in Mexico, Guatemala, Belize, Honduras, and El Salvador.

What you are thinking of is the Lowland Abandonment, a period of time in which the area the Maya live went under a sociopolitical change and some cities were emptied while others grew. The reasons are still unclear why this happened. The old hypothesis stressed environment as the only factor, probably drought or crop failure. However, from excavations, we know that not all cities experienced drought or crop failure, but were still abandoned. Other hypotheses include an ideological change, shifting trade patterns, ritual abandonment, political instability, disease, and warfare. There is no one reason, there are no multiple reasons. There is no consensus among scholars and perhaps there never will be. However in the years to come we may get a fee more answers as more scholars are shifting from the Classic period to Epiclassic and Postclassic and comparisons are done to better understand what happened.