Available information on clinical characteristics and post-operative outcomes in children with very severe obstructive sleep apnea (OSA) is limited. Our study evaluates the clinical features and polysomnographic (PSG) variables that predict post-operative outcomes in children with an obstructive apneal hypopnea index (AHI) of more than 25 events/hr. In this study from a single tertiary care center, we performed a retrospective chart review of patients with an AHI > 25/hr, who underwent tonsillectomy and adenoidectomy (T&A) between January 2016 and September 2021. In total, 50 children were included in the study: 26.0% (13/50) of children experienced post-operative respiratory events and four children needed intubation and ventilator support. Compared with children without respiratory events, children requiring post-operative respiratory interventions were younger (4.4 ± 5.2 vs. 8.0 ± 5.2 years; p = 0.04), had higher pre-operative AHI (73.6 ± 27.4 vs. 44.8 ± 24.9; p < 0.01), lower oxygen nadirs (70.0 ± 13.0% vs. 83.0 ± 7.0%; p < 0.01), and had lower body metabolic index Z-scores (−0.51 ± 2.1 vs. 0.66 ± 1.5; p < 0.04). Moderate to severe residual OSA was identified in 70% (24/34) of children with available post-operative PSG; younger children had better PSG outcomes. Our study shows that post-operative respiratory events are frequent in children with very severe OSA, particularly with an AHI > 40/h, younger children (<2 years of age), lower oxygen saturation (SpO2), and poor nutritional status, necessitating close monitoring.