By default, Procore will equip your project with weather from Weatherunderground.com based on the project address or latitude/longitude coordinates. Because this is a third-party software, sometimes the service will go down. You can check the status of weatherunderground here: Weatherunderground Status Page.
If you see the message below, this is not an error on your project or in Procore, and you can navigate to wunderground.com and type in your location to view your weather. This is not a permanent error, and you will only need to wait until the service is back up and running for it to be resolved (it is usually resolved within a few hours).