By the time KH2 comes around, Axel has basically already 'betrayed' Saix and chose other friendships over him. I totally understand by KH2, Saix doesn't care for Axel and is extremely bitter.
Honestly, it's easy to assume that Saix couldn't care less about Axel after his demise, but there's some things you have to consider. Saix has been Norted, he's led to believe that Nobodies cannot have hearts and he's lost his "friend" of the Organization. Despite his dangerous loyalty to the Organization, Axel hasn't really been the most collaborative friend to Saix.