A while back, I posted a command line batch file (in this post) that would log the time stamp each time the Internet went down and up, which you can use in the meantime.
Since the TestMy beta, I see it monitors whether the connection is down or up. For example, when I turn on Aeroplane mode, the TestMy page displays a "Connection failed" pop-up at the bottom and once I take off Aeroplane mode, it shows "Online" briefly:
In this case, it would just be a matter of this module recording the timestamp each time the connection goes down (such as in a Cookie). When the connection goes up, it just needs to send this timestamp along with the restored time to the server.