The beetle did not originally eat potato. It fed on buffalo bur and related wild solanaceous plants in the south-western United States and Mexico, and shifted onto cultivated potato as the crop spread west in the mid nineteenth century, then moved east across the continent within about two decades.
Resistance followed control. Paris green, an arsenic compound, worked from the 1860s until resistance emerged; DDT worked from the 1940s until resistance emerged in the early 1950s; the pattern repeated through organophosphates, carbamates, pyrethroids and neonicotinoids. Documented resistance now spans a large number of compounds across all the major classes deployed against the species.
Several traits make the beetle unusually good at this. It has a large detoxification gene repertoire, high fecundity with hundreds of eggs per female, and adults that overwinter in soil and can enter a facultative diapause, sometimes for more than a season, which lets a resistant population sit out an unfavourable year rather than being eliminated.