What is the reason that havdalah can be performed until Tuesday in the evening at sundown? Why did chazal choose that specific day?
Rabbi Eli’ezer Melamed writes:
If one did not make havdala over a kos on Saturday night, whether due to circumstances beyond his control such as a soldier on a mission, forgetfulness, or even on purpose, according to the majority of Rishonim (Rambam, Tosafot, Rosh), he may make havdala until the end of Tuesday, since the first three days of the week are linked to the previous Shabbat.
It is explained in the Kitzur Shulchan Aruch, 96:15:
If you forgot, were unable, or purposefully failed to recite Havdalah on Shabbos night, you may do so until the end of Tuesday. However, do not recite the berachah over the besamim or the candle, only the berachah, "borei peri hagafen" and the berachah, "Hamavdil." Once Tuesday has past, Havdalah can no longer be recited, because the first three days of the week are called "the days after Shabbos" and are considered the end of Shabbos, whereas the last three days are called "the days before the coming Shabbos" and have no relationship to the Shabbos past.
It seems to me that Rabbi Ganzfried is saying that we tend to refer to Sunday, Monday, and Tuesday as “the days after Shabbos” in our everyday speech and this is the reason why we are still able to recite Havdalah until then.