I still haven't pinpointed what causes this problem (except that it always happens, sooner or later) but I have just found that once it has happened, I can drag the top icon to a different location in the launcher and the problem stays with the icon rather than staying for whatever is at the top.
Say Nautilus was top and loses the tooltip, I drag it to third place in the list so that Firefox is now top. Firefox has a tooltip but Nautilus doesn't.
I still haven't pinpointed what causes this problem (except that it always happens, sooner or later) but I have just found that once it has happened, I can drag the top icon to a different location in the launcher and the problem stays with the icon rather than staying for whatever is at the top.
Say Nautilus was top and loses the tooltip, I drag it to third place in the list so that Firefox is now top. Firefox has a tooltip but Nautilus doesn't.