The series was originally canceled after /shows/the-killing/season 2, but Fox TV Studios kept the show alive, triggering AMC to order the /shows/the-killing/third season. The studio also made a deal for exclusive streaming rights with Netflix during the process. Rating played a part in the previous cancellation as well.
AMC had this to say about the cancellation.
"We have made the difficult decision not to move forward with a fourth season of The Killing. We want to thank our great partners at Fox Television Studios, creator Veena Sud, an extraordinary cast and the dedicated fans who watched."
Fox TV Studios also commented on the decision.
"Fox Television Studios is extremely proud of all three seasons of The Killing. We're especially gratified to have orchestrated a unique deal with AMC for Season 3 that included a bold partnership with Netflix. While we would have loved to produce a fourth season for AMC, FTVS is immensely grateful to everyone involved with this moving series: our brilliant cast, led by Mireille Enos, Joel Kinnaman and /shows/the-killing/Season 3's Peter Sarsgaard; our stellar executive producer, Veena Sud; a remarkable writing and producing team; and a tireless, dedicated crew. Most of all, FTVS thanks the terrific fans of The Killing, who communicated their appreciation for the show throughout its run."
The studio is planning on shopping other networks, but another resurrection is unlikely.