Unable to use multiple SDL windows

I’ve mentioned a few times the Delphi control I’m working on to embed
an SDL window in a form. Well, I’ve got it working, and it works really
well… until I try to use two of them. Then whichever one was created
first works just fine, and the other initializes properly but won’t draw
anything. Calling SDL_SelectRenderer, SDL_CreateTexture and
SDL_RenderPresent all give the right values, but nothing ever appears.
This happens no matter which renderer I create for my windows.

Has anyone else had trouble with multiple windows?