Brain states such as sleep, anesthesia, wakefulness, or coma are characterized by specific patterns of cortical activity dynamics, from local circuits to full-brain emergent properties. We previously demonstrated that full-spectrum signals, including the infraslow component (DC, direct current-coupled), can be recorded acutely in multiple sites using flexible arrays of graphene solution-gated field-effect transistors (gSGFETs). Here, we performed chronic implantation of 16-channel gSGFET arrays over the rat cerebral cortex and recorded full-band neuronal activity with two objectives: (1) to test the long-term stability of implanted devices; and (2) to investigate full-band activity during the transition across different levels of anesthesia. First, we demonstrate it is possible to record full-band signals with stability, fidelity, and spatiotemporal resolution for up to 5.5 months using chronic epicortical gSGFET implants. Second, brain states generated by progressive variation of levels of anesthesia could be identified as traditionally using the high-pass filtered (AC, alternating current-coupled) spectrogram: from synchronous slow oscillations in deep anesthesia through to asynchronous activity in the awake state. However, the DC signal introduced a highly significant improvement for brain-state discrimination: the DC band provided an almost linear information prediction of the depth of anesthesia, with about 85% precision, using a trained algorithm. This prediction rose to about 95% precision when the full-band (AC + DC) spectrogram was taken into account. We conclude that recording infraslow activity using gSGFET interfaces is superior for the identification of brain states, and further supports the preclinical and clinical use of graphene neural interfaces for long-term recordings of cortical activity.