I had a similar problem. I have solved it but am reporting it here because it definitely appears to be a bug.
I opened an afpub file, edited it, printed to PDF, then tried to save it. Message: Failed to save document. Save failed because the file could not be created. Do you wish to save the document to a new file? Clicked Save As, entered new file name. Message: Failed to save document. Save failed because the file could not be written to. It actually created the file with 0 bytes. Obviously I was worried the file might have been corrupted and not open again. However I closed the file without saving, and closed Affinity Publisher too. Fortunately I was still able to open my file again, edit it and save it.
