Tachanun begins with viduy (בגדנו אשמנו). The Baal Shem Tov zt'l teaches (Bereishis 22:24), ואת מעכה is roshei teivos of כסא עד מגיע תפילה אחר ודוי הכבוד, "Viduy after Shemonah Esrei reaches Hashem's throne."
A chassid told the Rebbe of Radishitz zt'l that he had lost most of his money. The Radishitzer asked, "Do you say tachanun?" Ashamed, he admitted that he hadn’t said tachanun for many years. "How many tachanuns are you missing?" Together, they calculated and realized that he was missing thousands of tachanuns. The Rebbe told him, "From now on, you must be cautious and say tachanun. Additionally, you must say all those tachanuns that you missed. If you do that, your mazal will come back to you. But if you miss even just one tachanun you owe, you won't get your yeshuah."
The man followed the Rebbe's instructions. It took a few weeks, but he said all the tachanuns he owed and was cautious about saying tachanun in the tefillos. His mazal improved, and he became wealthy. He came several times to Radishitz and generously gave to the Rebbe's household.
The Radishitzer Rebbe's son, Reb Hillel, repeated this story and added that his father's counsel was very logical. Because the Mishnah (Kiddushin 82:) states that people don’t have parnassah due to aveiros. As it states, "Reb Shimon ben Elazar said, 'Did you ever see animals or birds with a profession? Yet they have parnassah easily, without hardship. They [the animals] were created to serve me, and I was created to serve Hashem. Shouldn’t I have parnassah without hardships? Rather, it is because I did bad deeds. Therefore, I lost my parnassah." Aveiros is the root that lessens parnassah; therefore, saying viduy, which removes aveiros, helps restore one's parnassah.
Rava said to his students (Brachos 35:), "Please, don’t come to me [to learn Torah] during the months Nisan and Tishrei so that you won't be busy with your parnassah the entire year." According to its simple meaning, Tishrei and Nisan are the primary months to work in the field. He told them to work in their fields those months, so they would have the entire year free to study Torah. According to our discussion, we can explain צחות בדרך what Rava was telling them: Parnassah comes from tachanun and viduy. In the months of Tishrei and Nisan, we don’t say tachanun. Rava told his students that on those days, the only way to get parnassah was to work—literally. But for the rest of the year, they can earn their parnassah via tachanun.
The Arizal instituted saying (Tehillim chapter 86) לדוד תפילה on weekdays, before the של שיר יום, and he urges us to say it with a lot of kavanah.
Someone told the Shinover Rav about his financial problems. The Rebbe asked him whether he says לדוד תפילה every morning. The man answered that he didn’t. The Shinover Rav told him to say that chapter the amount of times he skipped it, and then he would have parnassah. And that is what happened.
There was a mageifah (epidemic) in a town near Stolin, and many young people were dying, r'l. The Beis Aharon knew that this community was lax with tachanun. The Beis Aharon sent them a telegram stating they should accept on themselves to be cautious with tachanun. They did so, and the plague ended.
Rebbe Shlomke Zvhiller zt'l said to the renowned Karliner chassid Reb Yehoshua Hershel Halutovsky, "I saw the Beis Aharon zt'l in a dream, and he asked me why people are lenient with tachanun and skip it." Reb Yehoshua Hershel asked, "How do you know it was the Beis Aharon?" Rebbe Shlmoke replied, "I saw the Beis Aharon when I was three years old."
Saying רחום והוא, the longer tachanun, on Mondays and Thursdays, has an extraordinary power. The Yaavatz teaches, "It is tested and proven, and it is known to the elders of the generation, that saying רחום והוא [Mondays and Thursdays] with a minyan annuls bad decrees."
Students of the Chasam Sofer zt'l said, "The hisorerus, the tears, and the teshuvah that can be seen by the great rabbanim at the highest moments of the yomim nora'im (like by tekiyos shofar and kol nidrei) was seen every Monday and Thursday when the Chasam Sofer said tachanun."
In a village near Belz, there was a Yid who ran a bar (a kretchmer). His routine was to close the store at one o'clock a.m. One night, at one a.m., he told everyone to leave, which they did, except for one person who was drunk like Lot. The tavern owner went over to him and told him to leave. The drunk got up and stumbled towards the door but tripped over a table leg, hit his head on the floor, and died.
The tavern owner was terrified. If people find out that a goy died in his shop, he would be held responsible. His life was in grave danger. He quickly left his shop, locked it outside, and rushed to Belz to speak with Rebbe Yehoshua of Belz zt'l. The Belzer Rebbe told him, "Go next to the corpse and say the והוא רחום (the long tachanun said on Mondays and Thursdays)." He said רחום והוא tearfully and with immense kavanah. When he finished, the goy stood up and left the store. The goy went to the place where he worked and lived. As soon as he entered his workshop, he fell to the ground, dead.
The tavern owner returned to Belz to thank the Rebbe. He asked, "If tachanun is so precious and powerful, why are Yidden lenient with it? Why do they seek opportunities to avoid saying it?" The Rebbe replied, "Do you want all goyim to come back to life?" Such is the power of tachanun!
