According to Wikipedia, the State passes a law in 1881 saying "Whereas, confusion of practice has arisen in the pronunciation of the name of our state and it is deemed important that the true pronunciation should be determined for use in oral official proceedings.
And, whereas, the matter has been thoroughly investigated by the State Historical Society and the Eclectic Society of Little Rock, which have agreed upon the correct pronunciation as derived from history, and the early usage of the American immigrants.
Be it therefore resolved by both houses of the General Assembly, that the only true pronunciation of the name of the state, in the opinion of this body, is that received by the French from the native Indians and committed to writing in the French word representing the sound. It should be pronounced in three (3) syllables, with the final "s" silent, the "a" in each syllable with the Italian sound, and the accent on the first and last syllables. The pronunciation with the accent on the second syllable with the sound of "a" in "man" and the sounding of the terminal "s" is an innovation to be discouraged."
In other words, it's the law...