Redistribute live stream (re-stream/re-broadcast video from IP camera)

I have an IP camera that acts as its own web server. It can only support 20 connections and it crashes pretty much daily because of this.

To get around this, I have a streaming web server set up and ready to capture the feed and redistribute it so essentially there is only ever one connection to the camera itself; the dedicated server handles the load.

Does anyone know how to capture the feed and make it available on my site?