Adaptive probabilistic modeling of the EEG background is proposed for seizure detection in neonates with hypoxic ischemic encephalopathy. The decision is made based on the temporal derivative of the seizure probability with respect to the adaptively modeled level of background activity. The robustness of the system to long duration "seizure-like" artifacts, in particular those due to respiration, is improved. The system was developed using statistical leave-one-patient-out performance assessment, on a large clinical dataset, comprising 38 patients of 1479 h total duration. The developed technique was then validated by a single test on a separate totally unseen randomized prospective dataset of 51 neonates totaling 2540 h of duration. By exploiting the proposed adaptation, the ROC area is increased from 93.4% to 96.1% (41% relative improvement). The number of false detections per hour is decreased from 0.42 to 0.24, while maintaining the correct detection of seizure burden at 70%. These results on the unseen data were predicted from the rigorous leave-one-patient-out validation and confirm the validity of our algorithm development process.