Where the heck is this coming from? Is it just me who is hearing this more frequently? "Please may I" is fine of course but what's wrong with "please would you?" or "please could you?"
It doesn't really make sense, I don't think, in that "may" is asking for permission - one could ask in the first or third person for permission but it just doesn't work in the second person.
Feel free to criticise the grammar or punctuation in my post, there's a lot of it and it's late at night but you get the general point I hope. Language evolves etc etc but I just can't quite square this one!