Birth asphyxia (BA) is one of the most serious birth complications affecting infants and can result in severe disabilities including mental retardation, cerebral palsy, and epilepsy. Animal models of BA and subsequent hypoxic-ischemic encephalopathy (HIE) are important to characterize functional and behavioral correlates of injury, explore underlying mechanisms, and assess the potential of novel therapeutic strategies. Using a non-invasive, physiologically validated rat model of BA and acute neonatal seizures that mimics many features of BA and HIE in human infants we studied (i) the temporal development of epilepsy with spontaneous recurrent seizures (SRS) in the months after the initial brain injury, (ii) alterations in seizure threshold and hippocampal EEG that may precede the onset of SRS, and (iii) the effect of prophylactic treatment with midazolam. For this purpose, a total of 89 rat pups underwent asphyxia or sham asphyxia at postnatal day 11 and were examined over 8–10 months. In vehicle-treated animals, incidence of SRS progressively increased from 0% at 2.5 months to 100% at 10.5 months after asphyxia. Unexpectedly, post-asphyxial rats did not differ from sham-exposed rats in seizure threshold or interictal epileptiform discharges. Treatment with midazolam (1 mg/kg i.p.) after asphyxia, which suppressed acute symptomatic neonatal seizures in about 60% of the rat pups, prevented progressive increase in the incidence of SRS regardless of its effect on neonatal seizures. This antiepileptogenic effect adds to recently reported prophylactic effects of midazolam on BA-induced neuroinflammation, brain damage, behavioral alterations, and cognitive impairment in the rat asphyxia model of HIE.