Which term describes a habit that is ingrained over a long period?

The term that describes a habit that is ingrained over a long period is "inveterate." This word specifically refers to something that has become established over time, often suggesting that it is hard to change or remove. For example, an inveterate smoker is someone who has been smoking for many years, indicating a deep-rooted habit.

The other options do not convey this particular meaning. "Indefatigable" refers to someone who persists tirelessly, while "inscrutable" describes something that is difficult to understand or interpret. "Insurmountable" relates to obstacles that cannot be overcome, which does not align with the concept of long-standing habits. Thus, "inveterate" is the most fitting choice to describe such habits.