Losing Button.Click events after first partial postback in UpdatePanel

I have a Page that has a single instance of a UserControl that itself has a single UpdatePanel. Inside the UpdatePanel are several Button controls. The Click event for these controls are wired up in the code-behind, in the Init event of the UserControl.

I get the Click event for the first button I push, every time, no problem. After that, I only get Click events for one button (SearchButton) – the rest are ignored. I have included the code for the control below – for sake of brevity, I have excluded the click event handler methods, but they are all of the standard "void Button_Click(object sender, EventArgs e)" variety. Any ideas?

<asp:UpdatePanel ID="PickerUpdatePanel" runat="server" UpdateMode="Conditional">
    <ContentTemplate>
        <asp:Panel ID="Container" runat="server">
            <div>
                <asp:TextBox ID="PickerResults" runat="server" style="margin-right: 3px;" SkinID="Plain" />
                <asp:Image
                    ID="LaunchPopup" runat="server" ImageUrl="~/images/icons/user_manage.png" 
                    ImageAlign="Top" BorderColor="#294254" BorderStyle="Dotted" BorderWidth="1px" 
                    Height="20px" Width="20px" style="cursor: pointer;" />
            </div>
            <asp:Panel ID="PickerPanel" runat="server" DefaultButton="OKButton" CssClass="popupDialog" style="height: 227px; width: 400px; padding: 5px; display: none;">
                <asp:Panel runat="server" id="ContactPickerSearchParams" style="margin-bottom: 3px;" DefaultButton="SearchButton">
                    Search: <asp:TextBox ID="SearchTerms" runat="server" style="margin-right: 3px;" Width="266px" SkinID="Plain" />
                    <asp:Button ID="SearchButton" runat="server" Text="Go" Width="60px" SkinID="Plain" />
                </asp:Panel>
                <asp:ListBox ID="SearchResults" runat="server" Height="150px" Width="100%" SelectionMode="Multiple" style="margin-bottom: 3px;" />
                <asp:Button ID="AddButton" runat="server" Text="Add >>" style="margin-right: 3px;" Width="60px" SkinID="Plain" />
                <asp:TextBox ID="ChosenPeople" runat="server" Width="325px" SkinID="Plain" />
                <div style="float: left;">
                    <asp:Button ID="AddNewContact" runat="server" SkinID="Plain" Width="150px" Text="New Contact" />
                </div>
                <div style="text-align: right;">
                    <asp:Button ID="OKButton" runat="server" Text="Ok" SkinID="Plain" Width="100px" />
                </div>
                <input id="SelectedContacts" runat="server" visible="false" />
            </asp:Panel>
            <ajax:PopupControlExtender ID="PickerPopEx" runat="server" PopupControlID="PickerPanel" TargetControlID="LaunchPopup" Position="Bottom" />
        </asp:Panel>
   </ContentTemplate>
   <Triggers>
        <asp:AsyncPostBackTrigger ControlID="AddButton" EventName="Click" />
        <asp:AsyncPostBackTrigger ControlID="SearchButton" EventName="Click" />
        <asp:AsyncPostBackTrigger ControlID="AddNewContact" EventName="Click" />
    </Triggers>
</asp:UpdatePanel>

public partial class ContactPicker : System.Web.UI.UserControl
{
    protected void Page_Init(object sender, EventArgs e)
    {
        SearchButton.Click += new EventHandler(SearchButton_Click);
        AddButton.Click += new EventHandler(AddButton_Click);
        OKButton.Click += new EventHandler(OKButton_Click);
    }

    // Other code left out
}