Well, you can use a Trigger for your Update Panel & do the Needful.
I'm just adding the Code for Trigger below:
<asp:updatepanel id="updReater" runat="server">
Here is your repeater control
<asp:asyncpostbacktrigger controlid="Button1" eventname="Click" />
In the above lines of code I'm considering your Button Id as 'Button1' & Targeting it's 'Click' event for Async Postback.
So Just add these few lines of Code & your job will be done.