I have signed documents before without any issues. I was also able to easily clear my signature when necessary. I was able to do these steps before and after the issue I am describing below.
Issue: When trying to save my signature on a document, I got the following error message:
After this, my signature was somehow saved on the document, but is showing as an invalid signature. Thus, I can clear/delete it and nobody, including myself, can edit this document.
It looks like your PDFs are also opened in another app or are on a drive in a folder that does not have write permission. Make sure that the same PDFa are not also opened in a browser, or id you have both Reader and Acrobat installed, in the one which is other than the one you're using for signing. Try to reboot your machine, open just Acrobat, so no other app is running, and try to sign saving to a local hard drive. If it is successful, then something happened on your installation that prevents Acrobat to save. Saving to a network drive with limited permissions might be one of possible reasons.