Call it the coffee paradox. The brewed beverage has never been more popular, but the price of beans is at its lowest point in over a decade and down by a quarter since October.

A pound of wholesale arabica beans, the premium variety favored in most coffee shops, has been selling for less than $1 since early March on the Intercontinental Exchange in New York, below what many producers say it costs to grow and process. Coffee drinkers might not have noticed any difference in price, given the prevalence of the $5 latte.

What...