How did show Shomer Israel become part of our daily tachnun? Clearly it happened in the 1800's. Prior to that it was just for slichos and Mondays and Thursdays (see magen avraham תרפה;ב....the very end as far as when to say shomer Yisroel. Also see aruch hashulchan קלא;ט.) See Jewish liturgy by Ismar Elbogen and Raymond Sheindlin. Thank you
This Beurei Hatefillah article is fairly extensive on the history of the piyut.
The article mentions that the piyut didn't start appearing in Siddurim as part of the daily tachanun until the 1700's. In earlier Siddurim, it was, in fact part of Tachanun, but to be recited only on fast days. In 1863, Siddur Dover Shalom Nusach Ashkenaz mentions that many congregations do say it daily, but even that Siddur suggests to say it only on fast days. This was also Vilna Gaon's position.
The article suggests that this piyut as well as the longer one, ה אלקי ישראל, recited by many on Mon. and Thurs., may have been inspired by phrasing of part of Tachanun mentioned in Siddur Rav Amrm Ga'on.