This is a brand new installation of APE14. When I try and close a project - either by File > Exit or clicking the top right "x" - I get stuck with the "Save changes to ___________ before closing." I click "yes," and then nothing happens. So I try to close again. Repeat. And even after I've saved it ~10 times, if I press "no," the edits don't save. I have rebooted several times.
Have you named your project and then used File/Save to save it?
If you do that, you've saved and you can close your project.
If the project is not saving, something is up with your system -- possibly related to your system's configuration, the directory you're saving your project files to or the amount of free, clean, freshly defragemented space on your hard drive.