fall off

Old English feallan (class VII strong verb; past tense feoll, past participle feallen) "to fall; fail, decay, die," from Proto-Germanic *fallanan (cf. Old Frisian falla, Old Saxon fallan, Dutch vallen, Old Norse falla, Old High German fallan, German fallen), from PIE root *pol- "to fall" (cf. Armenian p'ul "downfall," Lithuanian puola "to fall," Old Prussian aupallai "finds," literally "falls upon").

Most of the figurative senses had developed in Middle English. Meaning "to be reduced" (as temperature) is from 1650s. To fall in love is attested from 1520s; to fall asleep is late 14c. Fall through "come to naught" is from 1781. To fall for something is from 1903.