How long do potato plants live?

Gardening novice here. I planted a row of potatoes on Memorial Day weekend. They came up about 3 weeks later. Now a couple of them are getting droopy and the lower leaves are yellowing. The rest, which were planted later, are still fine.

Have they simply reached the end of their lifespan? Should I start digging?

And is it too late to hill potatoes? I did hill them all, but the hills are flatter now than they were at first?

Irish potatoes have a definite lifespan. When they reach maturity, the vines usually fall over, start yellowing and then dry up. For good storage, I prefer to dig after the vines die. Ther are quick maturing, medium season and late season cultivars. Here I have to plant an early maturing type and dig them in June. In cooler climates, September is the month to dig. As long as the potatoes are not exposed to the sun, there is no advantage to hilling them now. Should any be poking through the top of the soil, cover them either with soil or mulch to prevent greening.

Thanks for the info, Farmerdill.

Yeah, I think 2-3 of my potato plants have reached the end of their span. It rained today, and all the potato plants perked up except those couple, which are yellowing and falling over. Perhaps I should stop watering them?

I have stopped watering my oldest potato plants, the ones that are falling over and turning yellow. I scooped around their hills for potatoes. I didn't find any, although it's possible that my critters excavated them already.

How deeply did you dig for the potatoes?

I only excavated the hill I'd piled up around the plants, so it wasn't more than 2-3 inches. After the plants expire completely I'll dig deeper into the ground for them.

I always loved digging for potatoes as a kid. It was like seeking buried treasure. (Aaarrrr!)

I tried grabbling for a few new potatoes today and finally found one, about 3 inches down. The German Butterballs are a long season potato that I planted late this year.
I figured it was a bit early to harvest much, but I'm feeling more confident that there will be more when we are ready to harvest at the end of the month.

I didn't get my first potatoes into the ground until Memorial Day weekend, so it's only been three months. I figure they don't have more than 2-3 weeks left before a freeze hits.

We planted our chitted out seed potatoes on the second or third weekend in June. You've got a couple of weeks head start on me!
The community garden had the lottery for garden beds on Memorial Day. We spent two weekends preparing the soil and excavating the potato trench before we could plant. Forunately we don't get hard freezes here. We'll be harvesting the rest of the spuds at the end of the month.