Hello, it is possible to work without an internet connection. Spine requires a connection to our servers when you first install the Spine Launcher so that it may download the version of Spine that you would like to work in. After that, it should be possible to work offline.
If you're seeing that message pop up repeatedly, could you reinstall Spine with the latest launcher from your License Page?
And if that does not fix the issue, please reply to this forum post with your Spine log file, which can be found here: Spine Troubleshooting: spine.log