Probably about 3 - 3.5 months before your average first fall frost would be the latest. Some varieties take longer than others. What varieties are you planting? They will sprout and grow faster in warmer summer weather but you want them to be forming the potatoes after the weather and soil cools off in mid September into October.

Note: a frost will kill the top growth but the potatoes themselves should be OK as long as the soil doesn't freeze. You can mulch the bed deeply to moderate the soil temperature and delay harvest somewhat.