When you try to overwrite a file, yEd first saves your diagram to a new (temporary) file, then renames the new file to replace the file you want to overwrite. This is done to prevent corrupting existing files if an error occurs while saving your diagram.
Now, in your case, yEd successfully saves the diagram to the temporary file but then renaming the temporary file fails.
Unfortunately, there is little that can be done about this problem. yEd is a Java application and uses Java's I/O framework to rename files. Alas, this I/O framework does not work well with network shares.
Your best option is to always save to your local machine and then use Windows Explorer or some other Windows-native tool to copy the corresponding file from your machine to other machines in your network.
