Using approach from How to customize the package editor interface?How to customize the package editor interface?
CopyFile @@ ( FileNameJoin[ {#, "SystemFiles", "FrontEnd", "Palettes", "BasicMathAssistant.nb"} ] & /@ {$InstallationDirectory, $UserBaseDirectory}) SetOptions[ NotebookOpen@%, { Saveable -> True, ClosingAutoSave -> True (*thx to Mr. Wizard*) } ] When you move/resize/open another tab, the palette state will be saved.