Selected="True" to your list item will solve your problem.
<asp:DropDownList ID="ddlPageRowSize" EnableViewState="True" runat="server" AutoPostBack="True" OnSelectedIndexChanged="ddlPageRowSize_SelectedIndexChanged">
<asp:ListItem Selected="True" Value="10">10</asp:ListItem>
<asp:ListItem Value="20">20</asp:ListItem>
<asp:ListItem Value="50">50</asp:ListItem>
<asp:ListItem Value="100">100</asp:ListItem>
</asp:DropDownList>
please use the following code.
protected void Page_Load(object sender, EventArgs e)
{
if (Session["PageSize"] != null)
ddlPageRowSize.SelectedValue = Convert.ToString(Session["PageSize"]);
}
protected void ddlPageRowSize_SelectedIndexChanged(object sender, EventArgs e)
{
Session["PageSize"] = ddlPageRowSize.SelectedValue;
}