Set style= "display:none;". By setting visible=false, it will not render button in the browser. Thus,client side script wont execute.
<asp:Button ID="savebtn" runat="server" OnClick="savebtn_Click" style="display:none" />
html markup should be
<button id="btnsave" onclick="fncsave()">Save</button>
Change javascript to
<script type="text/javascript">
function fncsave()
{
document.getElementById('<%= savebtn.ClientID %>').click();
}
</script>