Elementary my dear Watson. Onion sets will not rot because of cold ergo it must have been something else that caused the problem. A disease, bacteria or fungus of some sort may be possible though onions are really very hardy and resistant to attack. The most likely cause of death, I reasoned, was drowning. Clay soil is the last to dry out.
Onion sets planted in a clay soil that then receives an inch of rain are likely to be in trouble.
I'm assuming that no one would plant sets in soupy clay but that could be an incorrect assumption, I suppose. If you have a clay soil, put the organic matter to it. Make a lot of compost and work it into the soil. Use a lot of bulky materials that are not high in nutrients like horse manure with wood shavings, hay mulch, leaves and the like. The organic matter breaks down into a magical ingredient called humus that is important in all soils but essential in clay.