Thanks for the comment, Knut. The equations for phi in IIT take into account the transition matrix of the network and wouldn't be affected by the inputs being similar over a long period of time. Perhaps a future theory of consciousness will take this into account!

Remember that the task, however cognitive, does not determine the consciousness according to IIT. As the unfolding argument shows, a task (that is, an input-output function) can be recreated with any level of phi.