"The problem was that the sag occurred slowly, rather than in the first hour of being erect",

This makes sense to me. If you went to sleep before sunset, for example, it might be dry and sunny. Later in the night humidity and possibly rain are added to the equation. The tent stretches and getting out to tighten things up would be unpleasant.

I typically go to bed early and have experienced this with all my nylon tents from time to time, even if I tighten things up before going to bed. I look for tents and have made some tents that address this problem by having a lot of room between the tent and the fly. Some sagging can then occur without the fly and tent touching each other and creating a point of wetness inside the tent.

I also have an REI tent that has, if I recall correclty, a polyester material for the fly. It doesn't sag much, if any, when wet. When I've made shelters from the blue woven cheap tarps I've always been impressed by how little they stretch dry or wet. When I replicate the design with nylon it shapes up quite differently due to the stretch.