<form id="form1" runat="server">
    <%=DateTime.Now.ToString() %>
    <asp:ScriptManager ID="ScriptManager1" EnablePartialRendering="true" runat="server"></asp:ScriptManager>
    <asp:UpdatePanel ID="UpdatePanel1" runat="server" UpdateMode="Conditional" ChildrenAsTriggers="true">
                        <%--<Triggers>
                            <asp:AsyncPostBackTrigger ControlID="student" EventName="TextChanged" />
                        </Triggers>--%>
                        <ContentTemplate>
                        <asp:TextBox ID="student" OnTextChanged="student_TextChanged" AutoPostBack="true" runat="server"></asp:TextBox>
                        <asp:Label runat="server" ID="message"></asp:Label>

protected void student_TextChanged(object sender, EventArgs e)
    {
            bool existStudent = CheckStudent(this.student.Text);//ищем в базе

            if(true == existStudent)
                 this.message.Text = "такой студент уже есть в базе";
            else     
                 this.message.Text = "допустимо";
    }

<%--<Triggers>
      <asp:AsyncPostBackTrigger ControlID="student" EventName="TextChanged" />
</Triggers>--%>