I got it. It can be done in the following way. The key is updating the readyState flag to false in AfterExitEditModeHandler.

//////////////////////////

var readyState = true;

window.onbeforeunload = checkProgressState;

function checkProgressState(){

if (!readyState){

message = "WARNING: Your data is not saved, if you choose to exit your information may be lost.";

return message;

}

else

{

readyState = true;

}

}

function HandleExitEditMode(gridID, cellID) {

readyState = false;

}

 ///////////////////

If you want this alert to be suppressed in SaveButtonClick, then OnClientClick of that button, update the readyState variable to true.