From 息(いき) (iki) + 遣(つか)い (tsukai, “連(れん)用(よう)形(けい) (ren'yōkei, “stem or continuative form”) of the verb 遣(つか)う (tsukau).”).
いきづかい • (ikizukai) ←いきづかひ (ikidukafi)?