I had the same symptoms with my Acorn Squash and it turned out to be Bacterial Wilt:

"Affected plants may first exhibit wilting of the leaves, which eventually spreads downward until the entire squash plant is affected. It differs from wilting caused by vine borers in that all leaves will be affected rather than sections of the plant as you might see with vine borers. In fact, an entire vine can wilt within only a couple weeks after infection. Typically, the fruits of affected plants will be wilted or poorly shaped. As is also the case with pumpkins, squash wilt does not occur as quickly as it does with other vine crops affected with bacterial wilt."

Read more at Gardening Know How: Squash Wilting And Dying: Signs Of Squash Wilt

The plants can't be saved and since the bacteria can be spread by squash bugs and other insects, they need to be removed and disposed of away from the garden as soon as possible to prevent the spread to other curbits (squash, cucumbers, pumpkins).

The other possibility is squash vine borer caterpillars, but they affect just one part of the plant, and you can usually see their sawdust-like droppings at the base of the branches.

Looks like SVB to me, but that may just be my PTSD talking. Check all around the stem for a damaged area that looks almost like it has sawdust coming out.

Thanks for the ideas. I will check for 'sawdust'.

If it's bacterial wilt, do I have a hope of growing healthy pumpkins here again, or is the problem in my soil and likely to persist next year?

The age-old question here -- where are you? If you're on the west coast, it ain't SVBs. But a whole vine dying sounds a lot like SVBs. If ALL the vines eventually wilt and die, it's bacterial wilt. If ONE vine wilts and dies, it's probably SVB.

I am close to Detroit MI. The whole vine is now gone and there's no sawdust to be seen. I think it must be bacterial wilt. Thanks everyone for helping to diagnose!

Do a search on google for svb frass under images (NOT FOR SQUEAMISH) to see what people mean by sawdust.

Question for the pros:. Is it possible to bury some parts of the stem of the pumpkin vine to encourage secondary or even a third set of roots as a backup root system in case the svb grub damages the main stem and causes it to not be able to function (derive what it needs from roots)?

Janice... it largely depends on the variety. Some root along the vine all on their own, others will do so when buried, yet others just won't. Here's a recent pic I took of a Costada Romanesco zucchini I grow...

As you can see, this pepo routinely sends out roots along the vine hoping to find soil.