Oh I see, you are using a single instance of Kinovea and alternating between a capture screen and a playback screen, correct?
It does save the capture folder, even between sessions, but when you open a new capture screen in the instance it starts from the default state (actually even this should work but I think it's because of opening a player screen in between that it lose the capture screen info).
The new workflow is that you would use a dedicated window for capture, and a different one for replay. Doing this it will remember everything, the camera, the capture folder, the position of the window, etc. It will be ready to go as soon as you start.
Same for the replay, the window will remember the observed folder, the playback speed, etc. Typically if you have two cameras and two replay you would have 3 windows, two capture and one dual replay. It's better to save to different directories otherwise the automatic replay can't tell which file to load. The replay window will also automatically bring itself to the foreground when it loads a new file.