I'd cut the bare branches back. Some years you get some dieback like that on the branch tips, often when the first freeze arrives extra early and the trees haven't gone dormant yet. That happened to mine last year.

If your trees have survived May's rainfall, I expect the clay must drain well enough.

In their native setting, they often grow in dry washes and dry creeks that only have water flowing through them in the monsoon season, so we know they can handle wet soil for at least part of the year. I doubt they'd be happy in waterlogged soil year-round.

My original desert willow was planted around 2003 or 2004 and is in the worst clay soil we have up near the house. It drains terribly slowly. Despite that, the tree has done well. The one I planted more recently is in a sandier soil that drains better. While the soils in area where they are natives leans more towards being limestone-based, sandy/gravelly or caliche clay types, they grow pretty well in sand, sandy loam, clay loam and even fairly dense clay. I guess the question is how much rainfall they can handle in dense clay and this might be the year we get an answer to that question.

If it helps any, they are related to trumpet creeper, yellow bells and catalpas, so if you can grow any of those in your clay [I realize yellow bells (Tecoma stans) are only annuals here], it is likely that you can grow desert willow.

Thanks Dawn I'll trim it back