There are many reasons that The Legend of Korra proved controversial with fans, but perhaps one of the most radical ways it shook up the world of Avatar itself came with the finale of Book Two. The spirit of Raava torn from her body and destroyed by the villainous Unalaq, in the wake of the climactic battle, Korra's connection to the Avatar State seemed irreparably severed.
For the rest of the show Korra endures hardships without the guidance or power of her past lives, but looking back over the series reveals that this separation isn't as permanent as it seems. Korra could very well contact her past lives, and may even be able to reestablish her connection to them.
Much of the second season of Korra built up the mythology behind the Avatar cycle, describing how it started with the first Avatar Wan fusing with the spirit of light, Raava, who reincarnated into a new body after each Avatar's death. When Raava was temporarily destroyed, Korra watched in horror as every past Avatar seemingly vanished before her eyes, starting with her immediate predecessor Aang and traveling through Roku and Kyoshi and all the others before reaching Wan's disintegrating form. The dramatic scene tolled with finality as it just did not seem that the Avatars would come back ever again.
Korra herself seems to doubt that she will ever reconnect with her lives, proceeding through the rest of the series and the comics without ever attempting to do so. The book The Legend of Korra: An Avatar's Chronicle by Andrea Robinson and illustrated by Sora Medina was even set up as a diary created by Korra to pass on her memories in case her own experiences did not pass on to the next Avatar, but for all the doom and gloom there may be hope after all.
Firstly, it is notable that Korra's connection to the past Avatars seemed to be what was destroyed, rather than the spirits of the past Avatars themselves. While the vision Korra saw watched each of the Avatars disintegrate, there is little reason to believe that the spirits themselves are intrinsically tied to Raava. Throughout the entire franchise, the Avatars are seen residing the Spirit World without being tethered to Raava herself. Aang visited Roku there and even connected with Roku's dragon Fang, the Fire Avatar's animal companion who was at one point visible in the material world to the spiritually-attuned Iroh.
Iroh himself shows that an individual's spirit can persist in the Spirit World in the same season where Korra's connection was severed. Book Two also featured Tenzin on his own journey in the Spirit World sharing an emotional moment with his father Aang in the Fog of Lost Souls, all occurring when neither Korra or Raava were present. Not only to spiritual masters like Iroh persist beyond their mortal lives within the Spirit World, but the Avatars were shown doing so repeatedly.
In fact, no piece of the canon could be more valuable to the discussion than Escape from the Spirit World, which almost single-handedly settles the issue.
Escape from the Spirit World was a canonical online game set between Book Two and Book Three of Avatar: The Last Airbender during the moments where Aang still struggled to return to life following Azula's attack at Ba Sing Se. His life in the balance, the story involves Aang reconnecting with the past four Avatars in order to restore his connection. In the story, he journeys through the Spirit World finding Roku, Kyoshi, Kuruk and Yangchen and hearing each of their stories. And by the end, he does exactly what Korra still needs to do.
The drama of Korra's connection to the Avatar cycle being destroyed is an understandable thing for the show to opt for, but the past Avatars are such rich and interesting characters that it would be a shame to close them off from inclusion in all future stories.
The world of Avatar already makes it clear that those characters are not completely gone, and there is even sensible way for Korra to go through a brand new journey to reconnect with them. Whether it be in a novel, a comic or a future show, it seems that for all of Korra's great accomplishments she may have one of her greatest missions still ahead of her yet.