Toad Suck is the name for a ford on the Arkansas River, near where Hendrix is located. In the olden days, steamboats and barges on the river sometimes had to stop there to wait if the river was running low. The crews would tie up their boats, and while waiting, they visited the tavern. The local citizenry, displeased by the sometimes unsavory crowd, were fond of saying "they suck on the bottle 'til they swell up like toads." Thus, the name Toad Suck stuck.
That's their story, and they're sticking to it.