Key points The effects of short‐term (ST; 10 days) and long‐term (LT; 30 days) intermittent hypoxia (IH) on blood pressure (BP), breathing and carotid body (CB) chemosensory reflex were examined in adult rats. ST‐ and LT‐IH treated rats exhibited hypertension, irregular breathing with apnoea and augmented the CB chemosensory reflex, with all these responses becoming normalized during recovery from ST‐ but not from LT‐IH. The persistent cardiorespiratory responses to LT‐IH were associated with elevated reactive oxygen species (ROS) levels in the CB and adrenal medulla, which were a result of DNA methylation‐dependent suppression of genes encoding anti‐oxidant enzymes (AOEs). Treating rats with decitabine either during LT‐IH or during recovery from LT‐IH prevented DNA methylation of AOE genes, normalized the expression of AOE genes and ROS levels, reversed the heightened CB chemosensory reflex and hypertension, and also stabilized breathing. Abstract Rodents exposed to chronic intermittent hypoxia (IH), simulating blood O2 saturation profiles during obstructive sleep apnoea (OSA), have been shown to exhibit a heightened carotid body (CB) chemosensory reflex and hypertension. CB chemosensory reflex activation also results in unstable breathing with apnoeas. However, the effect of chronic IH on breathing is not known. In the present study, we examined the effects of chronic IH on breathing along with blood pressure (BP) and assessed whether the autonomic responses are normalized after recovery from chronic IH. Studies were performed on adult, male, Sprague–Dawley rats exposed to either short‐term (ST; 10 days) or long‐term (LT, 30 days) IH. Rats exposed to either ST‐ or LT‐IH exhibited hypertension, irregular breathing with apnoeas, an augmented CB chemosensory reflex as indicated by elevated CB neural activity and plasma catecholamine levels, and elevated reactive oxygen species (ROS) levels in the CB and adrenal medulla (AM). All these effects were normalized after recovery from ST‐IH but not from LT‐IH. Analysis of the molecular mechanisms underlying the persistent effects of LT‐IH revealed increased DNA methylation of genes encoding anti‐oxidant enzymes (AOEs). Treatment with decitabine, a DNA methylation inhibitor, either during LT‐IH or during recovery from LT‐IH, prevented DNA methylation, normalized the expression of AOE genes, ROS levels, CB chemosensory reflex and BP, and also stabilized breathing. These results suggest that persistent cardiorespiratory abnormalities caused by LT‐IH are mediated by epigenetic re‐programming of the redox state in the CB chemosensory reflex pathway.