The biggest stockout problems in my life are those where an inconvenience turns into a big mess. If you can expand your thinking to that problem, I'm very interested.
Specifically:
Toilet Paper
Diapers
Diaper Wipes
Paper Towels
Cat Litter
Laundry Detergent
Sanitary Napkins / Tampons
Auto-coffee refill is something I can avoid. Diaper stockout -- the horror!