You will need to create a Windows Firewall rule. Go to Control Panel -> All Control Panel Items -> Windows Firewall. Click Advanced settings on the right-hand side, click Outbound rules on the left-hand side, then click New Rule on the right.
On the next window, make sure you have Program selected and click Next. Select the button for This program path: and click Browse. From here, you'll need to navigate to the .EXE file for Illustrator. It'll be under C:\Program Files (x86) (w/o the x86 if you're not running 64-bit Windows) and possibly within the Adobe sub-folder.
Once you've found the .EXE file, click Next, Block the connection, apply it to Domain/Private/Public networks, give it a name, and click Finish.