ASP.NET dynamically created controls and Postback

I know this question has been asked thousands of times, and I've struggled with it before, but for some reason, I can't accomplish what I want to accomplish... I have a dynamically added LinkButton that when clicked will dynamically add a control (in this example, a textbox) to the same panel. The intent is to continuously add on as many controls as times the LinkButton was clicked (i.e. I click it once, one box, then another click will give me 2 boxes, another click adds a 3rd). In the code below, I use the current date and time serialized to create a unique ID for each textbox control.

When I execute the code, clicking "Add Filter" will generate a new textbox, but once clicked again will create a new one, and dispose of the one before it. Instead, I want to persist the previous textbox as well as any data submitted within it.

Your help is appreciated.

In the aspx:

<asp:Panel ID="pnlFilter" runat="server">

</asp:Panel>

In the aspx.cs:

protected void Page_Init(object sender, EventArgs e)
{
        LinkButton lb = new LinkButton();
        lb.ID = "lbAddFilter";
        pnlFilter.Controls.Add(lb);
        lb.Text = "Add Filter";
        lb.Click += new EventHandler(lbAddFilter_Click);
}


void lbAddFilter_Click(object sender, EventArgs e)
{
    TextBox tb = new TextBox();
    tb.ID = "tb" + DateTime.Now.ToBinary().ToString();
    pnlFilter.Controls.Add(tb);
}