I wonder if they were wet. When I think of rot & potatoes, I think of too much water. Potatoes don't like wet feet.

Are these in pots?

No, they weren't in pots but I did have grass clippings hilled around them and with the intense heat we've had the past month I was watering them moderately about twice a week.

I had a similar experience -- only lost a couple of plants. I used grass clippings to mulch my potato bins. Heavy rains turned the clippings into a sodden mass that wouldn't dry out. My son took a lot of the mess out of the bins. The remaining plants look healthy and got mulched late (with weeds pulled from the garden). I have no idea what the potatoes will be like. I doubt I'm giving the potato bins a fair trial.