Thanks for reaching out. This error usually indicates that something is blocking the activation from returning to Topaz Photo AI.
Please disable antivirus, firewall, VPN, or proxy that may be on your computer. Then try activating again.
If that still does not work, open Topaz Photo AI, go to the menu bar on the top and click the Help > Open Log Folder menu option. Attach the logs files that you can see in the window that opens.