What is the literary device called when a comparison between two things continues beyond the initial point of comparison?

The term that refers to a comparison between two things that persists beyond the initial point of comparison is known as an extended metaphor. An extended metaphor not only highlights the similarities between the two subjects but also elaborates on this relationship throughout a passage, poem, or entire work. Rather than being confined to a single phrase or brief sentence, it allows for a deeper exploration of the comparisons being made, helping to convey more complex ideas or emotions involved in the relationship.

In contrast, a simile is a more limited comparison that typically uses "like" or "as" to draw parallels and does not extend beyond a single phrasing. A metaphor similarly creates a connection between two different things but usually does so in a more concise manner without the ongoing elaboration that characterizes an extended metaphor. Personification involves attributing human qualities to non-human entities, which is distinct from making comparisons altogether. Therefore, extended metaphor is the correct answer as it encapsulates the idea of sustained comparison throughout a text.