Why has "Caucasian" remained in use, while similar terms for other races have fallen out of use?

Group identifiers generally gain a pejorative connotation when the group they are attached to has a low or negative social status, particularly in relationship to the group that uses the identifier.

In other words, the word takes on the prevailing attitudes of the people who use it, regardless of dictionary definition. That's why older words seem so much more offensive --they carry the stench of outmoded attitudes.

The terms "Negro" and "Mongol" were used by Europeans to refer to other cultures, during a more xenophobic time, so the use of them now brings up memories of old stereotypes. Since the term "Caucasian" was applied to members of the in-group, and never used pejoratively, it never gained a pejorative connotation.