Thank you very much for your error report.
It seems like you are running into a problem in the Java runtime environment related to writing to network shares. Unfortunately, this means this problem probably cannot be fixed in yEd but has to be fixed by Oracle, the vendor of the JRE.
You can try to workaround this error by either saving to a local drive (and afterwards moving your file to the desired network share using e.g. Windows Explorer) or using the cross-platform file selection dialog instead of the native dialog. You can switch from the native dialog to the cross-platform dialog in "File" -> "Preferences", tab "General", option "File Chooser Dialog".