Why Does my IP Address Change?

I use my IP address to limit access to my web development site. I've noticed recently that my development site sees me at my actual IP address when I use www in the URL but a different IP address in another state when I leave out the www. Why is this?

are you using a redirection service to forward requests for the naked domain? that might explain it...

No redirection service. This is one of the many reasons that I have protected my development site from access by any IP address but mine.

There must be some sort of redirect or proxying going on because free accounts like yours on PythonAnywhere can only have one address and that the <username> address.