When onions are drying down their necks shrink first to keep pathogens out while they cure. If something (like moisture) gets in carrying bacteria, it can slowly rot them from the inside.

I vaguely remember that your onions got soaking wet while they were drying? If so, this could be the cause.
If not, i'm remembering wrong. There could be another problem like the tops were clipped before completely dry or the onions were bolted?

Madroneb-

Good memory!! I did have some onions get drenched while they were drying, but not these.

However, my wife did insist on clipping the tops "to save space." I'll go with that. Next year I'll take the shears away from her.

MY candy are keeping the best in 20yrs. I think it is because of the dry weather all yr.and they seem to be a little stronger tasting than normal. I have no idea how short your wife clipped yours but I clip mine a good 1\2 inch above the bend. By this time last yr. I had onions sprouting bad , to date I've had two sprout in a bu.&1\2
IMO the weather has more to do with growing and keeping onions than any thing. YOPPER

Yopper-

I think that the problem is that she clipped them before they were fully dried. She seems to want to trip off the tops, leaving about 2" as soon as we bring them in from the garden-"We don't want this part anyway and it just takes up room." Then, after they dry, she'll trim to about 1/2-1"

I have candy onions hanging in my basement now and they are fine. When I purchased them last summer they had at least a 2" stem on each one. I was told to hang them up in the basement, not touching which I have done. They are really looking good. When I need an onion, I just go down into the basement and clip one off my string. They don't show any sign of decay.