What word indicates something that is deep-rooted or habitual?

The word that indicates something that is deep-rooted or habitual is "inveterate." This term specifically refers to a condition or practice that has been established for a long time and is often difficult to change. It is commonly used to describe behaviors, habits, or tendencies that have become ingrained over time, suggesting a sense of permanence and reluctance to alter.

In contrast, the other terms have different meanings or connotations. "Instinctive" relates to reactions or behaviors that are driven by natural instincts rather than learned experiences, while "incessant" refers to something that continues without pause or interruption, typically used to describe actions that are ongoing rather than habitual. Meanwhile, "imminent" indicates that something is about to happen soon, which does not align with the idea of something being deeply rooted or habitual. Therefore, "inveterate" is the most appropriate choice for describing something that is established over time and often resistant to change.