Do you have internet access to your ArcGIS Online account? ArcGIs Pro is licensed/provisioned thru Online (or Portal) or thru the new License Manager option for concurrent-users. Unless you are using the License manager option, or have checked out the license for offline use, it seems to need ArcGIS Online to verify it is a valid license.
Manage ArcGIS Pro licenses—ArcGIS Pro | ArcGIS for Desktop
Also, make sure you maintenance has not recently expired for the ArcGIS Online....that could cause issues, but I would think it would be a different error message. To me, that just looks like an internet issue.