Change your confirm function like this:
function confirmDelete () {
return confirm("You're about to delete the account. Are you sure?");
}
And change your button to
<asp:Button ID="Delete_Account" runat="server" OnClick="Delete_Account_Click"
OnClientClick=" javascript return confirmDelete();" Text="Delete Account" Width="250px"
BorderColor="Silver" Font-Size="19px" Height="45px" Font-Bold="True"
Font-Names="Times New Roman" />
By returning false from client side script you're preventing server round-trip, your server click handler will never trigger.