http://iscoresports.com/

How come the clock continues to run on the web, even when it is stopped on the iPad, etc.

The clock on the web will reset to the time sent from the device each time a new event is sent from the device. The alternative is to have the clock only update when the device sends events, and not have it continuously running, but as long as you are scoring the game live, having the clock continue to run on the web with the re-synchs as new events come in seems to be the best experience for viewers.