The issue you observed is due to the fact that the RenderPartial(partialViewName, Model)
method renders the control explicitly and its popup images are not registered on the page.
To avoid that merely add RadStyleSheetManager in the partial view which will register the styles/images explicitly. I am attaching a test project to this forum thread for further reference (my partial view is in Views/RadTimePicker folder and is called RadTimePickerPartialView).
the Telerik team