I'd start by looking in the portals' logs (portaldir\logs\hostname\ latest log file; and the database as well). You potentially have an issue with the maximum size of Portals' WAL files. The default configuration has them set to 50MiB. Normally you'd configure your portal site to also have a webgisdr process running in one form or another. This cleans those files up. In the "arcgisportal\backup"-folder you'll also find a folder called WalArchive, this usually is, if a portal's clogged up, pretty safe to clean up. As a matter of fact: it's part of what webgisdr does.
But before you do go around deleting files, do check the logs, and do run webgisdr.
I get this error from time to time when I try to acess the Portal Website or when I try to open the MyOrganisation Tab. In both cases I was already logged in. If I now log out and afterwards log in I can access to Portal and all Sites without any errors.
Maybe the same works for you?
Thanks for the suggestion, I was logged on via SSO/IWA and hadn't thought to try logging off.
After signing out and back in my organization page displayed with no errors.