Hi,
I suspect that the PHP process running on the server does not have sufficient permissions to make changes to the plugin files. This could be either due to incorrect ownership values, or simply the file permissions are not set correctly. From the plugins perspective, you should try the manual update instead.
The ownership/permission issue must be solved on the server side via SSH or by contacting your hosting provider. It is also possible, that manual updating will resolve this, as the problematic files will be deleted and the new ones should get the correct permissions.