Use the DropDown() method instead on the instance of the menu in the ribbon:
((PopupToolBase)this.ultraToolbarsManager1.Ribbon.Tabs["Tab1"].Groups["Group1"].Tool["Menu1"]).DropDown();
The tools in the toolbars manager's Tools collection are root tools. They are never shown on screen. They contain common properties for all tool instances of the same type with the same Key. The DropDown method drops down a menu as if it had been clicked at its on-screen location. Since the root tools are never shown on screen, they can never be clicked and the DropDown method doesn't know where to open the menu. For more information about root and instance tools, the following help article has a section called "Root Tools and Instance Tools": http://help.infragistics.com/Help/NetAdvantage/NET/2008.2/CLR2.0/html/WinToolbarsManager_Terms_and_Concepts.html