Hi simflex,
You need to reopen the modalpopup on PostBack i.e. DropDownList change.
Please refer below sample.
HTML
<%@ Register Assembly="AjaxControlToolkit" Namespace="AjaxControlToolkit" TagPrefix="ajax" %>
<asp:Button ID="btnSearch" runat="server" Text="Submit" />
<asp:ScriptManager ID="ScriptManager1" runat="server">
</asp:ScriptManager>
<ajax:ModalPopupExtender ID="installAddress_MPE" runat="server" TargetControlID="btnSearch"
    PopupControlID="installnew" CancelControlID="btnClose" BackgroundCssClass="modalBackground" />
<asp:Panel ID="installnew" runat="server" CssClass="modalPopup" align="center" Style="display: none">
    <asp:Table ID="Table1" runat="server">
        <asp:TableRow>
            <asp:TableCell ID="TableCell3" runat="server">
                <asp:Label ID="installAddressHeader" runat="server" Text="New Installation Address Entry" />
            </asp:TableCell>
        </asp:TableRow>
    </asp:Table>
    <div id="divRebatable" class="popupdiv">
        <asp:TextBox ID="txt_toiletsizes" placeholder="Enter new Toiltet GPF" runat="server"></asp:TextBox>
        <asp:TextBox ID="txt_newAmount" placeholder="Enter amount" Width="100px" runat="server"></asp:TextBox>
        <asp:Button ID="btn_add" runat="server" Text="Add It" />
        <asp:Table ID="rebateTable" runat="server">
            <asp:TableRow CssClass="divHeader">
                <asp:TableHeaderCell ColumnSpan="4">Add Toilets</asp:TableHeaderCell></asp:TableRow>
            <asp:TableRow ID="allToilets" runat="server">
                <asp:TableHeaderCell>How many toilets?</asp:TableHeaderCell>
                <asp:TableCell>
                    <asp:DropDownList ID="ddlNumber" runat="server" OnSelectedIndexChanged="ddlNumber_SelectedIndexChanged"
                        AutoPostBack="true">
                        <asp:ListItem Text="--Select--" Value=""></asp:ListItem>
                        <asp:ListItem Text="1" Value="1"></asp:ListItem>
                        <asp:ListItem Text="2" Value="2"></asp:ListItem>
                        <asp:ListItem Text="3" Value="3"></asp:ListItem>
                    </asp:DropDownList>
                </asp:TableCell>
            </asp:TableRow>
        </asp:Table>
    </div>
    <br />
    <div>
        <asp:Repeater ID="DynamicRepeater" runat="server">
            <HeaderTemplate>
                <table border="1">
                    <tr>
                        <td>
                            Toilet Size
                        </td>
                        <td>
                            Model#
                        </td>
                        <td>
                            Date Upgraded
                        </td>
                    </tr>
            </HeaderTemplate>
            <ItemTemplate>
                <tr>
                    <td>
                        <asp:DropDownList ID="ddlToiletGPF" AutoPostBack="true" runat="server" OnSelectedIndexChanged="OnSelectedIndexChanged">
                            <asp:ListItem>--Select Any--</asp:ListItem>
                            <asp:ListItem Value="ASPSnippets" Text="ASPSnippets" />
                            <asp:ListItem Value="ASPforums" Text="ASPforums" />
                        </asp:DropDownList>
                    </td>
                    <td>
                        <asp:TextBox ID="ModelNumber" runat="server"></asp:TextBox>
                    </td>
                    <td>
                        <asp:TextBox ID="DateUpgraded" runat="server"></asp:TextBox>
                    </td>
                </tr>
            </ItemTemplate>
            <FooterTemplate>
                </table>
            </FooterTemplate>
        </asp:Repeater>
        <br />
        <asp:Label ID="lblSuccess" runat="server" Text=""></asp:Label>
    </div>
    <asp:Button ID="btnClose" runat="server" Text="Close" />
</asp:Panel>
<asp:Label ID="lblMsg" runat="server" Text="" /><br />
Namespace
C#
using System.Data;
VB.Net
Imports System.Data
Code
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        this.BindRepeater();
    }
}
protected void ddlNumber_SelectedIndexChanged(object sender, EventArgs e)
{
    installAddress_MPE.Show();
}
protected void OnSelectedIndexChanged(object sender, EventArgs e)
{
    installAddress_MPE.Show();
}
private void BindRepeater()
{
    DataTable dt = new DataTable();
    dt.Columns.AddRange(new DataColumn[3]{
                        new DataColumn("Toilet Size"),
                        new DataColumn("Model #"),
                        new DataColumn("Date Upgraded")
    });
    DropDownList ddl = DynamicRepeater.FindControl("ddlToiletGPF") as DropDownList;
    TextBox txt = DynamicRepeater.FindControl("ModelNumber") as TextBox;
    TextBox txt2 = DynamicRepeater.FindControl("DateUpgraded") as TextBox;
    dt.Rows.Add(ddl, txt, txt2);
    DynamicRepeater.DataSource = dt;
    DynamicRepeater.DataBind();
}
VB.Net
Protected Sub Page_Load(ByVal sender As Object, ByVal e As EventArgs) Handles Me.Load
    If Not Me.IsPostBack Then
        Me.BindRepeater()
    End If
End Sub
Protected Sub ddlNumber_SelectedIndexChanged(ByVal sender As Object, ByVal e As EventArgs)
    installAddress_MPE.Show()
End Sub
Protected Sub OnSelectedIndexChanged(ByVal sender As Object, ByVal e As EventArgs)
    installAddress_MPE.Show()
End Sub
Private Sub BindRepeater()
    Dim dt As DataTable = New DataTable()
    dt.Columns.AddRange(New DataColumn(2) {New DataColumn("Toilet Size"), New DataColumn("Model #"), New DataColumn("Date Upgraded")})
    Dim ddl As DropDownList = TryCast(DynamicRepeater.FindControl("ddlToiletGPF"), DropDownList)
    Dim txt As TextBox = TryCast(DynamicRepeater.FindControl("ModelNumber"), TextBox)
    Dim txt2 As TextBox = TryCast(DynamicRepeater.FindControl("DateUpgraded"), TextBox)
    dt.Rows.Add(ddl, txt, txt2)
    DynamicRepeater.DataSource = dt
    DynamicRepeater.DataBind()
End Sub
Screenshot
