Tzom Gedalya 5751 occurred on a Sunday, just as it is this year, 5775. In the Rebbe’s Sicha on that day the Rebbe said:
“Tzom Gedalya is one of the strictest and most important fasts… The reason being, that the downfall on this day was a great downfall: After the downfall of the Jewish nation which brought us the three fasts of Asarah B’Teves, Shiv’a Asar B’Tamuz and Tisha B’Av, which correspond to the steps leading to and the actual destruction of the Beis Hamikdash, G-d had mercy on the Jewish nation, and part of the Jewish nation was still able to stay in Israel, led by Gedalyahu Ben Achikam. However, on Tzom Gedalya, even this last ray of hope was extinguished, when Gedalya was killed.
This idea is emphasized with regards to Tzom Gedalya, which has a stringency with regards to the other fasts – for since it occurs immediately after Rosh Hashana, from a holiday of rest and enjoyment to a day of fasting and suffering, it is a greater suffering, as it says in Gemara that the Anshei Ma’amad would not fast on Sundays, as to not go from enjoyment to suffering…”
Sefer HaSichos 5751 Vol. 1 page 21
Where does this rumor start from?
In the biography of the renowned Chossid R’ Zalman Gurary OBM (RaZaG), on page 503-504, the following story is related:
“It was Rosh Hashana 5737 (1976), and in middle of the prayers R’ Zalman fainted, and it seemed that he has no pulse…
His children got really worried as they thought of Tzom Gedalya, knowing his arduous service of G-d on Rosh Hashana and the toll it took on a person of frail health like him, especially fearing what would happen on Yom Kipur. On Motzoei Rosh Hashana, during Kos Shel Bracha, his son R’ Itche Meir Gurary and son-in-law R’ Nochum Sternberg approached the Rebbe, and told the Rebbe that despite the frail health of R’ Zalman, he is still stubborn that he must fast on Tzom Gedalya. The Rebbe replied sternly “He must ask a Rov” and the Rebbe then added “In Lubavitch, Chassidim would not fast on Tzom Gedalya. If he wants to be a Chossid – he should not fast!”
The Rebbe, knowing with whom he was dealing, knew that this was the only way to get R’ Zalman to stop being stubborn and listen to his doctors. R’ Zalman relented, and agreed that he will only fast half-a-day.”
This is the only extant source to this “custom,” and we as Chassidim ought to follow the Rebbe, who fasted on Tzom Gedalya every year, recired Slichos, got an Aliyah, and said “Divrei Kibushin” to the assembled Chassidim, never hinting to the fact that Chassidim would not fast on Tzom Gedalya.