A few answers:
The Dover Shalom writes that each of the Avos attained a unique recognition of Hashem, Avraham through "gedulah," and Yitzchok through "gevurah," and Yaakov through each of his fathers' approaches plus his own (and therefore Yaakov has a vov by the mention of אלקים associated with his name).
Etz Yosef explains that it is following the instruction Dovid HaMelech gave to his son Shlomo (Divrei Hayomim 28:9) that he should arrive at his own knowledge of Hashem. Each of the Avos attained an understanding of Hashem through their own investigation, and not just as a reliance on the understanding of their predecessors. (Panim Meiros says a similar idea.)
The Lechem Rav explains this based on Bava Metzia daf פה, that Eliyahu serves the Avos in Ma'aras Hamachpela separately, because if they joined together it would "force" the redemption before its proper time. So too when we pray, and the lips of the Avos are moved through our prayers, we separate them to not have them pray together.