For some reason I have had problems updating via FTP due to a permission issue. I think I have got around it by using file manager on the server.
However, could you also update in the following way.
1.leave the child theme in place
2.diactivate / remove the main theme
3. re-upload the new version of the theme via WordPress
I wouldn’t really delete the theme because your widgets will be messed up and have to redo them and anything else you setup. Because even leaving the child theme in, you will more likely lose everything once you remove the parent theme because the child theme inherits the parent. If you are having issues with permissions, then this is something you should take up with your host’s support and find out what is happening. You should have full access with your FTP.