A fair amount of "what-if" discussion surrounds rocket engine failure at critical points in various crewed missions -- lunar ascent and trans-Earth injection on lunar landing missions, retrorocket failure on LEO missions.
A popular approach to managing these risks is to use a single engine made reliable through simplicity: hypergolic propellants and pressure feed. This has been quite successful.
Including uncrewed missions, when is the last time a mission-critical, pressure-fed, hypergolic engine failed to ignite on command in space? Some technicalities:
- I would not count a stuck circuit that was solved via something like a circuit breaker reset in short order, i.e. in less than an hour with no screwdriver-level intervention
- I would not count a single failing attitude thruster that didn't prevent a desired attitude change via other available thrusters
- I would count something like a single STS OMS engine failing a planned burn in a way that required using the other OMS instead