Why don't we say Uvah Letzion on Shabbos by Shacharis and say it by Mincha?
Moreover, we then commence to repeat it by Maariv. Why do we do that?
The Kol Bo Siman 40 and Rokeach Siman 362 say that we do not say Uva Letziyon by Shacharis on Shabbos due to the elderly people, pregnant woman, and expecting mothers that are there as we do not want to make them wait that much longer to eat. Therefore we say it instead at Mincha.
Regarding saying it on Motzei shabbos the Rokeach says it has to do with the fact that sinners are returning to Geheinom then.
A reason I have heard mentioned in the name of the Avudram (however I have been unable to locate) is that since they used to have sermons immediately prior to Mincha on Shabbos and Yom Tov and the end of the sermon was usually about redemption therefore we say Uva Letzioyon at Mincha.