Oh No! Lost my file!

Files which are used for undo (this is not exactly auto-save, but they are written on every undoable action) sit in your system temporary folder (e.g. on Linux it is /tmp). There is a built-in option to recover from these files: Help > Recover... which interactively reads them from the most recent to the least recent one. However, before recovering I would examine them using any text editor and would save somewhere to not-so-temporary folder either all of them or the one which looks promising. Otherwise, they are deleted automatically after one or two GanttProject restarts.