Hi Cliff Gibson,
Only a single tooltip might be visible at any given time and thus when you open the second one, the first one hides. This behavior is by design and will not be changed as changing it would defy the purpose of the control.
The purpose of a tooltip is to provide additional information for a given element. It is not meant to be used as a popup control or as a draggable panel. For this purpose we provide RadWindow and RadDock controls. Both of these controls allow more than one visible element of the kind on the page.
Our suggestion is to consider using RadWindow and RadDock controls.
the Telerik team