Hybrid outpatient clinics must expand access while maintaining reliable operational performance. This is difficult when telemedicine visits share clinical capacity with in-person care and are affected by infrastructure disruptions. Unlike service time variability, telemedicine disruptions can add consultation time or prevent visits from being completed. This paper studies how disruption conditions and appointment slot length affect such systems. An analytical model is developed to separate added workload from incomplete telemedicine visits and to derive a reference slot length for a given disruption setting. The mechanism is tested using a discrete-event simulation of a hybrid outpatient clinic with scheduled patients, walk-ins, emergencies, no-shows, and carryovers. Results show that short disruptions increase overtime and utilization, while longer disruptions reduce congestion because some telemedicine visits are not completed. Longer slots reduce waiting, but increase carryover by reducing daily appointment capacity. Resilient hybrid outpatient scheduling, therefore, requires balancing congestion, capacity, and telemedicine appointment completion.