The above code will not work because Delete function is a asynchronous call. You will need to modify the code to allow the call to be completed and invoking another delete afterward. Here is the modified snippet:

var i = 0;
var intervalObj;

function DeleteRow()
{
    var grid = ISGetObject("grdObj");
    var checkedRows = grid.RootTable.GetCheckedRows(); 
    if (checkedRows.length > 0)
    {
        intervalObj = setInterval(function()
        {
            if (!grid.IsInProgress)
            {
                if(i < checkedRows.length)
                {
                    var htmlRow = grid.RootTable.GetCheckedRows()[0];
                    var wgRowObject = grid.RootTable.ToRowObject(htmlRow);
                    if (wgRowObject.KeyValue != '')
                        wgRowObject.Delete();

                    i++;
                }

                if (i >= checkedRows.length)
                {
                    clearInterval(intervalObj);
                    intervalObj = null;
                    i = 0;
                }
            }
        }, 5);
    }
}

Thanks Glenn, that makes sense, and has solved my problem.