What attempts does Borden make to reconcile with Angier in Section 5, Part 2, and why?

Borden gives himself until the next season to figure out Angier's trick on his own, or he will put the rivalry asside and ask Angier directly. Unfortunately, Angier takes an absence to America, so Borden humbles himself by sending several messages in order to end the rivalry and make amends. Angier does not respond, so Borden resolves to proceed alone.