In short, in the WebSplitterPanel that contains the popup menu, please set the AllowPopup property to True.
Explanations:
Normally, the overflow style of a panel is set to auto. When there are too much content, scrollbars will be displayed on the panel. When a popup menu is displayed, and the area it occupies is outside of the panel, you have to scroll the panel in order to view the menu.
By setting AllowPopup to True, the overflow property of the panel, and its ancestor, is set to visible so that the menu can be displayed 'outside' of the panel area.
Beware that you should then make sure the content inside the panel should not overflow, otherwise they will be visible in adjacent panel and no scrollbar will be displayed.
Update: Please see the reply below for additional information regarding ASP.NET Menu control.