Let them go as long as possible - harvest when the vines are killed by frost. They need a long growing season, so hope for a late first frost.
To decide on harvest date, a sample of roots should be dug (usually by hand). U.S. No. 1 yield is maximized when a few jumbo roots are produced. At this stage of growth, more U.S. No. 1 (medium sized and maximum priced) and fewer canners (smallest sized and lowest priced) are produced, which results in the highest income from the crop.