Q. Why in Eretz Yisrael do they say pitum haketores before pizukai dizimra with korbanos and then repeat it at the end of davening?
A. Remoh (O.H. 132: 2) writes that one should recite Pitum Haketores in the evening and in the morning after the tefilah. He adds that there are those who avoid saying it during weekdays when people are hurried to go to work, out of concern that we may in our rush miss mentioning one of the spices that comprise it and incur in a most severe penalty. Mishna Berura (ibid. 17) explains that the reason of the ones who do recite it (Sefaradim) is because there is no penalty when one forgets only words unwittingly.
Arizal quoting from Zohar (Vayakhel 218b, Yalkut Meam Loez – Shemos p.168) mentions that pitum haketores should be recited three times a day, at the beginning and end of Shacharis and a third time at Mincha. (Od Yosef Chai – Miketz, Ben Yish Chai - Ki Tisa)
Otzrois Chaim (p. 319) citing Benayahu explains that they represent our three forefathers that instituted the tefilos. It is not said at Maariv since there are usually no korbonos at night.
Ben Yish Chai finds an allusion to the three recitations in posuk (Devarim 3: 29) and we settled in the valley opposite Beth Peor. The word "BaGai" or in the valley, hints to three times ("BaG") and eleven ("ai,") the number of the spices and ingredients that compose the ketores. The ketores is the cure for the ills and evils of Beth Peor.
Minhagei Eretz Yisrael (p. 108) and others point out that it is tradition to follow in Eretz Yisroel the minhag of the Arizal and Minhag Sefarad in a number of issues, given that many of the first kehilos were from that persuasion.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a