The Missouri Botanical Garden has a good write-up on this issue. IME some varieties are more resistant, and good cultural practices including planting deeply and having enough sun and moisture will help reduce the problem. I haven't ever had a plant killed by wilt, though I do have one that seems more susceptible.

While I don't wish to confuse the issue, I think a fair number of times what we assume to be clematis wilt really isn't what is horticulturally known as 'clematis wilt' but another wilt-type phenomenon that produces very similar symptoms.

I remember a few years back Miguel and I (any regs. remember Miguel?? What a generous and knowledgeable contributor to this forum. He is much missed!) had a long discussion about wilt-type diseases. The consensus was that in addition to the wilt pathogen, Ascochyta clematidina, cultural conditions can create similar symptoms and stem dieback. This occurs typically on young plants, where the top growth grows out of proportion to the root system or faster/larger than the root system can support and wilt and die back is a result. To the untrained eye (which includes mine!), the issue looks identical to wilt.

Regardless of the actual source of the problem, the situation is seldom fatal (as Babs indicates) and the vines will typically grow out of it given a few years of establishment. The cautions for planting deeply and pruning back hard for the first couple of seasons seem to forestall most problems, as these practices encourage a strong and healthy root system and multiple stem formation, which tend to reduce the severity of the issue, if not preventing it entirely.

Back in the days when I was acquiring and growing scores of different clems, I used to bring home various nursery 'returns' - vines that had been purchased but returned for refunds because of "wilt issues". Rather than discarding the vines, I took them home and planted and nurtured them. ALL returned to become beautiful, healthy vines. I personally have never experience wilt in my garden so I am hesitant to consider it a major problem - and if it does occur, it is very recoverable.

If you do believe wilt is an issue, typically just cutting the vine back hard (below any signs of dieback or to the base) and tending to the vine as normal will produce regenerated growth that is typically 'clean', although the problem could recur in subsequent years for a season or two. But the vine will eventually outgrow the issue.