1530s, "to break wind without noise," probably altered from obsolete fist, from Middle English fisten "break wind" (see feisty) + frequentative suffix -le. Related: Fizzled; fizzling.
Meaning "make a noise as of a liquid or gas forced out a narrow aperture" is from 1859, "usually with special reference to the weakness and sudden diminution or cessation of such sound" [Century Dictionary], hence the figurative sense "prove a failure, stop abruptly after a more-or-less brilliant start." But this sense is earlier and dates to at least 1847 in American English college slang, along with the noun sense of "failure, fiasco" (1846), also originally U.S. college slang, "a failure in answering an examination by a professor." Barnhart says it is "not considered as derived from the verb." Halliwell ("Archaic and Provincial Words," 1846) has fizzle (v.) as "To do anything without noise," which might connect the college slang with the older word via some notion of mumbled and stifled performance:
In many colleges in the United States, this word is applied to a bad recitation, probably from the want of distinct articulation, which usually attends such performances. It is further explained in the Yale Banger, November 10, 1846: "This figure of a wounded snake is intended to represent what in technical language is termed a fizzle. The best judges have decided that to get just one third of the meaning right constitutes a perfect fizzle." [John Bartlett, "A Collection of College Words and Customs," Cambridge, 1851]