Something may be interfering with the connection to the server.
As a test, can you completely disable any anti-virus, firewall, proxy or VPN. Sometimes even restarting your router may resolve this. Then restart eM Client and try again.
If that still doesn’t help, some apps turn off specific services that are required for licensing, so there are some you can check. Click on the Windows Start button and type Services. Open the Services option from the results. Check that both Cryptographic services and CNG Key Isolation are running. If they aren’t, start them.
Then try the activation again.