In what way will a shriveling stem ensure "freshness"? If the squash is mature, leaving it on the vine doesn't buy you anything, and may risk rotting. Freezing temperatures will also harm the fruit. Winter squash should be cured, off the vine, to allow water to evaporate and sugars to concentrate. When you harvest, keep a piece of dried stem on the squash. That seals the fruit better.

Thanks!

I also wipe them down with a weak bleach solution.

I think Donald is asking if it is better to "cure" the squash for storage on or off the vine, letting the vine die naturally or cutting off the squash while the vine is green. Suppose it depends on the weather.

I think the point is that once the stem is shriveled, the plant isn't going to supply anything to the fruit. That being the case, why leave it on the vine? You just risk freezes, pests, and rot.

I have a related question. My winter squashes (big landrace C. maximas) never really get the stems totally shriveled. The fruit set in late July or early August, so it has been at least 50 days since fruit set. The nights are getting pretty chilly now in late Sept, and I'm just not sure if I should take them in or keep them out longer, seeing as the stems still have green stripes visible in them. The part of the stem closest to the fruit is narrower than the rest of the stem: does that mean it's shriveling?