While the game itself will be sticking around online for people to continue playing, Battleborn will no longer be updated after the fall. In a message to their fans on the company's message board, Creative Director Randy Varnell announced that the final update for the game will happen sometime in the next couple months and that the game would remain online for the foreseeable future to allow people to come in and play the game. Below is a snippet from the message, which you can check out in full here.
As of this week, there will be no more Battleplans and there is currently no planned content after the Fall Update. Details of any future changes or news will be made on our forums or through social media, so keep your radars on. Never fear! Battleborn is here to stay. Nothing is changing with Battleborn, and the servers will be up and active for the foreseeable future. We announced the Fall Update for the game at PAX including some new skins, themed around some of your favorite Borderlands characters! That update will also include some updated title art (more full bar titles!) for the more significant challenges in the game, as well as some additional Finisher Boosts and Taunts. Also, there are minor balance changes in that patch.