"The meeting with the policeman never failed to amuse him."
"failed to amuse" mean is not amused or unsuccessful to amuse him?
* Not a teacher
Never failed to amuse means that the meeting with the policeman amused him every time.
If he met the policeman many times, then Meeting with or The meetings with would work better for me. The meeting with sounds like, for example, a scene from a film he watched many times.
Sir God's right- it means he was always amused.
1) The stand-up comedian failed to amuse him.
This means that he was not amused by the comedian.
2) The stand-up comedian never failed to amuse him.
In your context, as in my second example, there's a never before failed to amuse, so it means the opposite. He was amused by the comedian.