Slow leak that fixed itself?
In the end, it seems I had a badly applied patch that was leaking.

I dipped the tube in water (again) and there were small air bubbles coming from the edge of the patch, maybe one per second. I tore off the patch and installed a new one.

It leaked more when I rode the bike, likely due to the extra weight. When I wasn't riding it, the air loss was much slower which lead me to think that it had fixed itself. Also, my pressure checks were inaccurate, done with fingers only, which can't really tell the difference between 40 PSI (the minimum) and 75.