One of the strangest. Just to confirm...
When you Save Project File AS, by clicking the chevron to the right of the Home menu | SAVE icon on the toolbar, is this what you see?

All that's needed is to click SAVE and the VPJ file will be saved in the path shown - in this case that's DOWNLOADS.
Something on your PC seems to be thwarting your efforts. To see if there is disc corruption, from the elevated (administrative) Command Prompt, type this, then <enter>...
chkdsk C:\ /f
Answer YES to the prompt and restart the PC.
In Videopad click OPTIONS | DISK tab and Clear Unused Cache Files. Close VP. Restart it, then load the project. Any success?
And a newer version for you to try. Your info has been passed on.