Apparently notwithstanding the obligations that stemmed from their revelations. They moved to the distant inhospitable planet Hessra (their proverbial Ivory Tower) stopping all distractions from the outside world and society, cared only by their Secondaries.
In 174 BG the Cogitors came back in the matters, when they visited Salusa Secundus, seeking volunteers to replace their elderly Secondaries. Iblis Ginjo made several attempts to approach Vidad and ask his insight about the Butlerian Jihad, however he denied any position. Ginjo then appointed Keats and other volunteers to follow the Cogitors as their Secondaries and during the passing of years, try to join their side. They were blessed by Serena Butler and moved to Hessra. During that time, the new Secondaries provided the Cogitors with speakerpatches so that they could communicate without neural connection with them.
8 years later, Serena Butler visited the world and attempted to make the Cogitors join the side of the Jihad explaining that their neutrality is disastrous to humans. Vidad dismissed her saying that her explanations gave them much to ponder. They would consider her request and take whatever action they deem appropriate.
After the Titans abandoned the Synchronized Worlds and rebelled against Omnius, they operated a secret business supplying the cymeks with electrafluid. Unwilling to be dependent on them, Dante had established their own electrafluid-manufacturing facilities on Bela Tegeuse and Richese, but of inferior quality.
In 108 BG the Titans decided to leave Richese for Hessra in order to elude Omnius' attacks and claim the electrafluid facilities, they assaulted the planet. Agamemnon and Juno killed all five Cogitors (except Vidad who was absent to Salusa Secundus) and declared the planet theirs.