Most likely it's a security software that is causing the problem (anti-virus, anti-spyware, firewall etc.). I recommend making sure that GOG Galaxy is added to your software's trusted applications list (whitelist). How to do this varies, depending on the software.

Also, make sure that your account has administrator privileges, and that you have unrestricted access to the game installation folder.

If it doesn't help, please write to our Technical Support here. I'm sure that they will find the solution :)