in fact the onbeforeunload event supported in Firefox browser, but the window.event is not supported in Firefox.
 
So, we can use the following code to stop page from leaving:
 
    function SaveRemind()
    {
        window.event.returnValue= "input has not been saved, are you sure to leave?";   
}
 
But we should use the following code in Firefox to achieve the same effect:
 
    function SaveRemind()
    {
        return "input has not been saved, are you sure to leave?";   
    }
 
If you would like to save the user changes in onbeforeunload event, and don’t stop the page from leaving, we can use “window.confirm” function just like following code:
 
            if(window.confirm("Are you want to save data?"))
            {
                 document.getElementById("BtnSave").click();//you can write other codes for save data in this line, just like a AJAX call function.
                 window.alert("data has been saved");
            }
 
In your scenario, we also need to distinguish whether a post is back occurring or user leaving this page. Please check the following code in italic:
 
The full code of my test demo (work in Internet Explorer 6.0/7.0 and Firefox 3.0):
 
<%@ Page Language="C#" AutoEventWireup="true" CodeFile="Default11.aspx.cs" Inherits="Default11" %>
 
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
    <title>Untitled Page</title>
    <script type="text/javascript">
    var NeedAlert=true;//when postback occur (form’s onsubmit), needn''t alert.
    function SaveRemind()
    {
        if(NeedAlert)
        {
            if(window.confirm("are you want to save data?"))
            {
                 document.getElementById("BtnSave").click();//you can write other codes for save data in this line.
                 window.alert("data has been saved");
            }
        }
    }
    </script>
 
</head>
<body onbeforeunload="SaveRemind();">
    <form id="form1" runat="server" onsubmit= "NeedAlert=false;" >
    <div>
    </div>
    <asp:Button ID="BtnSave" runat="server" onclick="Button1_Click" Text="BtnSave" />
    </form>
</body>
</html>
 
    protected void Button1_Click(object sender, EventArgs e)
    {
        using (SqlConnection conn = new SqlConnection(@"Data Source=....."))
        {
            using (SqlCommand cmd = new SqlCommand("insert into Table1 values(''myname'',''myid'')", conn))
            {
                conn.Open();
                cmd.ExecuteNonQuery();
            }
        }
    }
 
One thing I need to mention is that, I am not sure about if user click “OK” button so quickly and the BtnSave.Click () can also make the data save in database. So, you’d better to write an asynchronous function call, just like AJAX to save the data.
 
If I’ve misunderstood the facing problem, please feel free to let me know.