There is no Shulchan Aruch about how often to say Yechi. However, it is clear that the Rebbe encouraged Chassidim to say Yechi every time after davening. When the Rebbe requested to go to the porch after Davening, the only event that happened is that Yechi was sung, and the Rebbe encouraged it and then returned to his room.
The fact that it is also announced at a Simcha or at the end of a Shiur or other occasions is based on a Sicha of the Rebbe -- the famous Sicha which was said on the 28th of Nissan, 5751. It is the Sicha in which the Rebbe said, “I did everything I could possibly do... now I am giving it over to you…” The Rebbe expresses his pain in that Sicha about the fact that when ten people get together, they do not raise a storm to bring Moshiach. We can understand this in a simple way. If someone is ill, G-d forbid, when the family members get together, there is not a time when they will not mention a Bracha for their loved one, especially during a simcha where people are making L’Chaim. They announce the names of those who should be well because that is what is on their minds- they are obsessed with it. The Rebbe says that since we are supposed to be obsessed with the coming of Moshiach, how is it possible for ten people to be together and not take advantage of the opportunity to make a tumult about Moshiach? Therefore, Yechi is said at a Chasunah, and specifically at the Chuppah. The Chuppah is an especially auspicious time for the Chasan and Kallah. Of course, therefore, it is a time to announce Yechi. Any place where many people are gathered provides an opportunity to raise a storm about the revelation of Melech HaMoshiach, and to publicize the Rebbe’s prophecy that Moshiach is about to be revealed.
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