Concept:
The phrasal verb break down means to fail, collapse, or stop functioning successfully.
Step 1: Understand the context.
The sentence states that no compromise could be made.
This means the negotiations failed.
Step 2: Recall the phrasal verb.
\[
\text{Negotiations broke down}
\]
means
\[
\text{Negotiations failed.}
\]
Step 3: Choose the correct option.
\[
{\text{down}}
\]
Therefore,
\[
{\text{Option (A)}}
\]