The ASPxPopupControl does not allow a developer to prevent a PopupControl from being hidden when the CloseButton is clicked based on a custom criteria. A possible solution for this limitation is to use templates. You should add a button to the PopupControl's HeaderTemplate container and decide whether a PopupControl should be closed or not when this button is clicked.
<%@PageLanguage="C#"AutoEventWireup="true"CodeFile="Default.aspx.cs"Inherits="_Default"MasterPageFile="~/MasterPage.master"%><%@RegisterAssembly="DevExpress.Web.v8.1, Version=8.1.6.0, Culture=neutral, PublicKeyToken=79868b8147b5eae4"Namespace="DevExpress.Web.ASPxPopupControl"TagPrefix="dxpc" %><asp:ContentContentPlaceHolderID="ContentPlaceHolder1"ID="CC"runat="Server"><inputid="Button1"style="width: 325px"type="button"value="Click button to show PopupControl" /><br /><dxpc:ASPxPopupControlID="ASPxPopupControl1"runat="server"PopupElementID="Button1"ClientInstanceName="popupControl"ShowCloseButton="False"><HeaderTemplate><divstyle="text-align:right;"><inputid="btn"type="button"value="close"onclick="
if(document.getElementById('checkBox').checked)
popupControl.Hide();
"/></div></HeaderTemplate><ContentCollection><dxpc:PopupControlContentControlrunat="server"><labelid="lbl">Check CheckBox to be able to close the PopupControl by clicking the Hide button</label><inputid="checkBox"style="width: 32px"type="checkbox"/></dxpc:PopupControlContentControl></ContentCollection></dxpc:ASPxPopupControl></asp:Content>
<%@PageLanguage="vb"AutoEventWireup="true"CodeFile="Default.aspx.vb"Inherits="_Default"MasterPageFile="~/MasterPage.master"%><%@RegisterAssembly="DevExpress.Web.v8.1, Version=8.1.6.0, Culture=neutral, PublicKeyToken=9B171C9FD64DA1D1"Namespace="DevExpress.Web.ASPxPopupControl"TagPrefix="dxpc" %><asp:ContentContentPlaceHolderID="ContentPlaceHolder1"ID="CC"runat="Server"><inputid="Button1"style="width: 325px"type="button"value="Click button to show PopupControl" /><br /><dxpc:ASPxPopupControlID="ASPxPopupControl1"runat="server"PopupElementID="Button1"ClientInstanceName="popupControl"ShowCloseButton="False"><HeaderTemplate><divstyle="text-align:right;"><inputid="btn"type="button"value="close"onclick="
if(document.getElementById('checkBox').checked)
popupControl.Hide();
"/></div></HeaderTemplate><ContentCollection><dxpc:PopupControlContentControlrunat="server"><labelid="lbl">Check CheckBox to be able to close the PopupControl by clicking the Hide button</label><inputid="checkBox"style="width: 32px"type="checkbox"/></dxpc:PopupControlContentControl></ContentCollection></dxpc:ASPxPopupControl></asp:Content>