I had the same question, here’s how to fix
You just have the preferences set to close the window when the last tab is closed. Look at the menubar when you close the last tab. Does the application menu still say Photo Mechanic or Photo Mechanic Plus? If so, then the app is still running, it just doesn't have a main window anymore. You can change this behavior by unchecking the "Close contact sheet window when the last tab is closed" checkbox. Then what will happen is a new Untitled tab will appear when you close the last tab instead of closing the entire window.