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Very interesting! Thank you! There is another interesting piece of information about them. They are considered "almost" carnivorous. They attract insects to the flowers. They get trapped inside, and die. When the flowers fall off the insects are returned to the soil, where they become nutrients. Very interesting way of doing things.

It would seem, since these are affecting two of the same species, that there is a fungal infection present in the soil. You will have to cure this, if it is curable. This can be done by applying dolomitic lime, and wettable sulfur to all of the infected areas. This will kill off any infection that is able to be killed, and bring the soil back to proper pH. After about 2 weeks, you should be able to replant.

Here is an article that will give you more information on the care of these: https://www.gardeningknowhow.com/ornamental/vines/dutchmans-pipe/growing-dutchmans-pipe-vine.htm

I have answered the question on the original post.

This unique vine is hardy in zones 8-10.
It would not winter over in a cold climate.

https://www.gardeningknowhow.com/ornamental/vines/dutchmans-pipe/growing-dutchmans-pipe-vine.htm

Initially, the plant uses its energy mainly for growing new leaves, hence yearly new shoots are rather sparse, especially during the first few years. Foliage from May to November. The vine doesn't look “straggly” in winter, as the sparse new shoots keep their decorative light green color. The older, perennial shoots are light grey.
Pipe Vine are generally disease free.
From your image though I do think it appears to be a fungus issue.
I would use a fungicide on the vine and see if the appearance improves.

https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

This link will help you.

https://www.moretonbay.qld.gov.au/uploadedFiles/moretonbay/environment/vegetation/dutchmans-pipe-using-glyphosate.pdf