Generally, this is a result of the firewall/internet settings blocking the add-in. Please ask your system administrator for help. Here are some steps to make sure everything works properly:
Make sure you have installed all the Windows and Word updates available for you.
Make sure you have an active internet connection.
If you're using a controlled device, make sure external websites such as https://languagetool.org are not blocked.
If the problem persists, please try to install another add-in: Adobe Sign. If the Adobe add-in works, but the LanguageTool add-in doesn't, we know the issue is specific to LanguageTool.