I don't love you any more.
mean that my love dwindled till there was not any more of it left, focus(s)ing on the process, whereas
I don't love you any longer.
would mean that there came a day when I had to admit my love had ceased to be, focus(s)ing on that day's more or less sudden realisation rather than on the process which led (had led?) to that day?
How alive is the distinction between 'not any more / no more' and 'not any longer / no longer'?