No internet connection warning, when wanting to download library content

I bought a legal version of Logic Pro X, but it won't complete to download the library content. I keep getting the message:

Your computer must be connected to the Internet in order to download the Logic Pro sound library. Check your Internet connection and try again.

I uninstalled Logic and re-installed it. My Macbook is connected to LAN and my speed is almost 1GB Mbps.

I tried to install small portions of the library (electronic drumkit, only 500MB), but I still keep getting that message. There's 600GB of free space on my harddrive.

I've been googling this subject, installed an AppCleaner, but I keep getting that message. What can I do?