Interesting issue.... Based on the clockwise twining seen in your pictures, this appears to be a Japanese wisteria. Is is a named variety/grafted plant? Does it produce a lot of root suckers and, if so, do you allow them to remain and climb on the structure? You said in your original post that the vine is doing well - is any part of it visibly dead - i.e. no leaf or flower growth? Does the vine lose its leaves at some point in the year in your climate? (My two wisterias are just losing their leaves for the winter now....) If the vine loses its leaves at some point in your growing season, that's a good time to give it a close inspection. Since the support structure is also wood, it may well have rot too, so check it carefully (What kind of wood is the support structure?) Wisterias are pretty tough plants that can survive a lot of damage. If it is still producing healthy new growth from the stems that have split, I wouldn't worry too much about the vine. If there are areas where the vine is dead (i.e. no leaf or flower growth) I'd prune out the dead section and let nearby healthy growth fill the blank space. If there are suckers from above a graft union or if you normally let root sucker grow and they flower the same as the rest of the vine, you could use them to help fill in any dead sections too. If there is a nearby botanical garden or a commercial grower of the vines, you could ask them for further help in identifying the source of the problem and what to do. At this point, I wouldn't give up or the vine or assume it will die out. They are very tough plants and it would take a lot of damage to completely kill it! Do you have a picture of it in flower on the structure? If so, I'd love to see it....

O no! these look like what in Italy are called "processionarie"-the Bug Parade. Do not get near them-they really can cause allergic itching, if they are the same ones that we had. Now, I am against-totally against-any insecticides or herbicides, but these may require spray. Is there any trustworthy local source to which you can turn for advice? If they are only on a few plants, I'd say use long-handled clippers and a long-handled arm-extender-pincher that holds an open bag , and just clip off the branches that hold the nests/parading bugs, dropping them into the bags, and then trash them (not compost). Do NOT use any kind of insecticide unless you have on-hand,local, and professional advice. Insecticide can actually worsen the problem! Been there, done that...

Look for them at night with a flashlight

When I lived in a townhouse, I started a shaded native plant garden in the back and I was thrilled: my first real garden. I had researched Maryland native plants and found a researcher who was growing them. I was able to buy a few from her fledgling business... Then one day I noticed a few plants looked shorter, but not from the top. A few days later, right before my very eyes, I watched one of those plants disappear straight down, like a vacuum had sucked it down. I ran over and saw where the plant used to be was now a hole. Voles. Voles, voles, voles and the plants disappeared just like in the cartoon; I never would have believed it if I hadn't seen it with my own eyes. The next time I saw one of those, it became friendly with a pitchfork.