If I understand correctly you want the RadMenu item, containing the RadSearchBox, to stay opened after you click on it. Please, find the OnClientItemClosing event
documentation article, which shows how you can cancel the item's contraction.
If this is not the functionality you want to achieve, please explain your actions step-by-step (clicking on the RadMenu, searching in the RadSearchBox, etc.) and what you expect to happen at each step.
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