Step 1: Understanding the Concept:
This analogy is based on an antonym relationship, specifically linking a quality to an action that it cannot perform.
Step 2: Detailed Explanation:
EPHEMERAL means lasting for a very short time. To ENDURE means to last for a long time. Therefore, something that is ephemeral, by its very nature, cannot endure. The relationship is "a characteristic and the action it prevents."
Now let's analyze the answer choices:
\begin{itemize}
\item (A) insensitive: cooperate - An insensitive person may find it difficult to cooperate, but it's not an inherent impossibility.
\item (B) infirm: react - An infirm (weak) person might react slowly, but they can still react.
\item (C) ineffectual: proceed - Something ineffectual (not producing a desired result) can still proceed (continue); it just does so without success.
\item (D) inelastic: stretch - Inelastic means not elastic; unable to be stretched and return to its original shape. By its definition, something that is inelastic cannot stretch. This is a perfect match.
\item (E) inflammable: ignite - Inflammable means easily set on fire, so it is something that can ignite. This is the opposite of the required relationship.
\end{itemize}
Step 3: Final Answer:
The pair "inelastic: stretch" has the same "quality that prevents an action" relationship as "ephemeral: endure".