chuck up the sponge (v)
drop by the wayside (v)
drop out (v)
fall by the wayside (v)
give up (v)
quit (v)
throw in (v)
throw in the towel (v)

Definition: give up in the face of defeat of lacking hope
Example: In the second round, the challenger gave up.

drop out (v)

Definition: withdraw from established society, especially because of disillusion with conventional values
Example: She hasn't heard from her brother in years--he dropped out after moving to California.

drop out (v)

Definition: leave school or an educational program prematurely
Example: Many students drop out because they are not prepared for our challenging program.