When numbering a multistory stair on section only the numbers in first stair are tagged, all the stairs on above stories keep without number tags. I think it's a revit error that must be addressed.
Another thing with stair numbering is that they don't work on sketch stairs. I don't know why, because in their property Revit show the numbers treads you have, and the majority of sketched stairs have their runs properly drawn.
Maybe stair with double run, Y or fork shape are awkward to numbering their tread, but you can maintain the same number for treads with the same heights.