License key validation requires an internet connection to communicate with the RC Astro license servers. Make sure your computer is connected to the internet and that you can browse to the RC Astro site. Very infrequently the license servers are offline for maintenance. This usually lasts just a few minutes.
If the plugin still can’t seem to connect and you are on a Windows machine, the Windows Defender Firewall may be blocking access. To allow it to connect, you’ll need to allow Photoshop or PixInsight to make connections through the firewall.
Here’s a guide for Windows 10: https://pureinfotech.com/allow-apps-firewall-windows-10/
And another for Windows 11: https://www.technipages.com/block-unblock-programs-in-windows-firewall/
On Linux and MacOS machines, make sure there isn’t some third-party software blocking access to the internet.
You may also need to make sure access is not being blocked by your network’s firewall. This may involve contacting your IT department if at work, or checking router/firewall settings if at home.