Welcome to the forum Marjorie.
Can you describe the rot in a bit more detail - which part of the stem and the appearance of the rot? I'm by no means an expert in potato diseases, but it sounds like either blackleg or sclerotinia...neither of which I've ever had to deal with, but my guess is it would be one or the other.
The real path to natural farming requires that a person know what unaltered nature is, so that he or she can instinctively understand what needs to be done—and what must not be done—to work in harmony with its processes. - Masanobu Fukuoka