The correct answer is C) Lube oil entering the air intake manifold. Lube oil entering the air intake manifold can prevent an auxiliary diesel engine from shutting down because the oil can contaminate the air/fuel mixture, disrupting the engine's normal combustion process. This makes it difficult or impossible to cut off the engine's fuel supply, which is a key step in shutting down the engine. The other answer choices, such as high inlet air temperature or exhaust back pressure, may cause operational issues but would not directly prevent the engine from shutting down.