It's very odd because it's only new page loads. Existing metrics pages I've been refreshing keep showing new data.
But I can't create a new session, even when remoted into an Azure-hosted VM. All our servers and services seem to be running fine; it just seems to be the portal.azure.com website that is impacted.
An easy way to validate this would be using fidler or similar to analyze the traffic that happens in the loaded page.