Provide event name to the trigger..Provide EventName="Click"
as it is a button..
<asp:UpdatePanel ID="UpDateGrid" runat="server">
<ContentTemplate>
<asp:Button ID="btnSaveInstitute" runat="server"
Text="Save" OnClick="btnSave_Click" CausesValidation="false"></asp:Button>
</ContentTemplate>
<Triggers>
<asp:AsyncPostBackTrigger ControlID="btnSaveInstitute" EventName="Click" />
</Triggers>
</asp:UpdatePanel>