I'm on Linux, using a window manager with virtual desktops. If I switch (back) to the virtual desktop where Task Coach was running, I can no longer find it. Where did Task Coach go?

Task Coach is probably minimized. Look for the little Task Coach icon in the system tray, click on it with your right mouse button and select 'Restore'. Apparently, switching between virtual desktops is implemented by sending a minimize event to applications. Unfortunately, Task Coach has no way to distinguish between minimize events caused by the window manager and minimize events caused by the user minimizing the window. If you run into this issue, you may want to change the setting 'Hide main window when iconized', see 'Edit' -> 'Preferences'.