Is it permissible to say 'Ya Rasool-u-Allah' (Address Muhammad (Sallallahu Alaihi wa Sallam))? Please answer with reasons, because it is much-debated question in subcontinent.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

As for saying "Ya Rasool-u-Allah: O Allah's Messenger", we have to present the following four states:
First, if one uses this expression as a form of Istighatha (seeking help) as saying: 'O Allah's Messenger! Dispel my grief or grant me health', this constitutes Shirk (polytheism), since it is a prayer for something that no one can grant except Allah.
Allah Says (interpretation of meaning): {And your Lord said: "Invoke Me, [i.e. believe in My Oneness (Islâmic Monotheism)] (and ask Me for anything) I will respond to your (invocation). Verily! Those who scorn My worship [i.e. do not invoke Me, and do not believe in My Oneness, (Islâmic Monotheism)] they will surely enter Hell in humiliation!"} [40: 60].
The Prophet (Sallallahu Alaihi wa Sallam) said: "Du'a (supplication) is (the essence of) worship" .
Since Du'a is the worship itself, it becomes a form of Shirk to address this Du'a to a human being, any human being.
Allah Says (interpretation of meaning): {And when they embark on a ship, they invoke Allâh, making their Faith pure for Him only, but when He brings them safely to land, behold, they give a share of their worship to others.} [29: 65].
This verse indicates that one who is in a serious need to Allah, prays to Him; and when he gets his need satisfied or becomes in safe state, he seeks His slaves' help and aid.
Second, if one uses this expression as a form of Tawassul (solicitation) as saying: 'O Allah's Messenger! Be my intercessor or intermediary with Allah to dispel my grief'. This form of al-Tawassul is also unpermitted.
Third, ivoking blessings on the Prophet (Sallallahu Alaihi wa Sallam) like saying, 'O Allah's Messenger! Blessings and Peace of Allah be upon you, this is recommendable'.
Fourth, mentioning the merits of a dead person as one says, 'O Allah's Messenger! I do bear witness that you reformed the people and guided them to the right path. I'd like you to know what people are doing now!' (i.e. after his death), there is no harm in such action as long as it is no more than mentioning his (Sallallahu Alaihi wa Sallam) good deeds and good features'. But, one should avoid crying out in grief wailing or tearing clothes, since such actions are Haram.
Allah knows best.