What is the term for being incapable of making mistakes or failing?

The term "infallible" specifically refers to the quality of being incapable of making mistakes or failing. It conveys an absolute certainty and an error-free state, often used in contexts such as doctrines, beliefs, or individuals who are perceived as incapable of error. This characteristic implies that the entity in question has an unerring nature, making it a precise fit for the definition provided in the question.

In contrast, while "perfect" suggests completeness and flawlessness, it may not always imply the absence of error in practical application. "Reliable" indicates dependability and the likelihood of consistently performing well, but it does not guarantee absolute correctness or infallibility. Similarly, "unfailing" suggests a persistence or the ability to never give way, but it can be more context-dependent and does not specifically denote the idea of being free from mistakes. This makes "infallible" the most accurate term for a state of being without error.