Aircraft need 6–8 minutes between landings on a single runway. Rain roughly doubles that. A one-hour heavy shower wipes out ~20 slots. Those flights get pushed back, and because the airport already runs near capacity there's no slack to absorb them — the delay propagates until midnight.
Queueing theory makes it precise. In an M/M/1 queue the mean wait scales as ρ/(1−ρ). As utilization ρ approaches 1, that blows up: at ρ = 0.95 the expected queue is already ~19 aircraft, and any disruption produces effectively unbounded delay. NAIA runs at ~95% on a good day.