I have Portal for ArcGIS working well at two locations. The biggest issue is that users get a print error when accessing an image service from an outside agency. I have attached a image of the error message.
If the background image is changes, printing seems to work fine. Both instances of Portal experience the same thing.
I have communicate with the agency, but have not found a solution - other than use a different service, which I would rather not do.
When printing, the machine hosting the printing tools used in the web application is making an outbound request to all URLs in your web application/webmap. It sounds like your ArcGIS Server machine doesn't have access to the URLs that are being printed, likely due to a firewall. On the Server machine, see if you can reach the REST endpoint in a browser:
If not, printing that service won't work.