We have never had much trouble with storing winter squash before, except when some left in an unheated garage froze during a particularly harsh spell, which ruined them rather quickly. This year, though, we have found the stems afflicted with grey mould. When harvesting the squash, it is critical to leave a certain amount of stem intact, as this area is most susceptible to rots. The appearance of grey mould on the stems is, therefore, rather worrying. It appears that many recommend the use of a dilute solution of bleach to wipe over the squash before storing, but I have never fancied the idea, nor previously found it necessary.
Once harvested, the squash are best moved to a warm, dry location for two or three weeks in order for the skins to cure thoroughly. Once hardened, they can be moved to a cool, dry area for longer term storage. Ours are being stored in an outbuilding, with an electric heater with thermostat to ensure it remains frost free, but it is perhaps a little damp. The wet and miserable weather does not help, either, but, perhaps more importantly, the squash were only cured for about one week, as we needed to clear them away for some house renovations. It seems that this may not have been long enough, especially for the stems to properly dry out.
Being somewhat uncertain of the best treatment, and still reluctant to apply chemicals, I took a blowtorch to the mouldy stems. This certainly dealt with the mould, but whether it will return again remains to be seen. Generally, the squash still appear to be sound so they may yet store successfully. At the moment, house renovations have left us without a kitchen for some weeks, and with several weeks to go, it would be a pity if we did not get to use them.