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.
get licenced for offline use...it is a pain otherwise..unless you really, really need AGOL for your work
But caution if you use/allow for offline use, and staff leaves or there is some other issue, it may be hard to "recover" the license without contacting tech support or customer service. (similar to allowing borrowing with concurrent licenses)
not a problem...I work alone...so I am not hard to find