If Aang broke off his connection with Roku, then how is the Avatar cycle maintained? Even if we assume that breaking the connection doesn't actually affect the reincarnation cycle, Korra still shouldn't be able to connect with her past lives? EVEN if we assume Korra can connect with all the other Avatars except Roku, it still doesn't explain how she saw a vision of Roku when Unalaq was attacking Raava.
Last warning. If you haven't finished reading The Rift, turn back now.
Aang repairs the Fire Amulet he broke and reconnects with Roku, regaining his ability to connect with his past lives in the process. This restores the cycle and is the reason Korra can also (Prior to Book Spirits) connect with prior Avatars.