I work in I.T. as a Network Engineer. Yes there could be routing issues with the internet providers. But most likely, in all my years in I.T., I would suspect this is a server performance problem. They might not have enough server power. That means hardware ie- processor, memory, and hard disk performance.
Websites that have alot of traffic are usually load balanced across several different hardware servers.
Michael
CEO- Mile-HI-RailroadPrototype: D&RGW Moffat Line 1989