I revisited the problem and looked at the 'donut'.
Select both the donut and the cutting plane and then select 'explode curve' from the context menu. Then select intersect with model. Cleanup as usual. Use 'reverse faces' to finish off the ends of the donut.
What is happening is that the cutting plane is not bisecting the circle entities, and so when one tries to delete these the model falls apart.
I tried the same with the branching pipework, which resulted in a cleaner cut and easier cleaning up. However, I still had to trace over lines either side of the vertical branch point to get the pipe thickness lines to sink in to the cutting plane. After that one can delete the plane.
Curious!
Kind regards,
Bob