I have heard that on the SMA it is possible for the diesel fire to go out on descent, which is why I believe they have a minimum descent power requirement.
On a liquid-cooled engine though, this is less of an issue because the cooling system can be thermostatically controlled to limit the rate of cool-down.
Having said that, since you can start and idle a modern diesel engine at the top of most mountains (FL100-120) I'd say the chance of losing ignition for a diesel engine because an inlet hose burst or fell off is pretty remote, especially under any reasonable power level that still remains. The beauty of a diesel engine though is that it doesn't rich misfire, hence the black smoke.