Tuning graphene conduction states with the remnant polarization of ferroelectric oxides holds much promise for a range of low-power transistor and memory applications. However, understanding how the ferroelectric polarization affects the electronic properties of graphene remains challenging because of a variety of intricate and dynamic screening processes that complicate the interaction. Here, we report on a range of slow electrical conductance relaxation behavior in graphene-ferroelectric field-effect transistors with the extreme case leading to the convergence of two polarization-induced states. Piezoresponse force microscopy through the graphene channel reveals that the ferroelectric polarization remains essentially unchanged during this conductance relaxation. When measured in vacuum, the conductance relaxation is significantly reduced, suggesting equilibration with adsorbates from the ambient atmosphere that can cause charge transfer to and from graphene to be the origin of the slow relaxation.