Stallions get 20 breedings per game year (real life month), so maybe he's hit the limit.

Refusal means your horse refused to take a jump. It's a penalty to the score.

Think of it as when your horse levels up it's having to adjust to higher, wider jumps with new things added, like double jumps or water hazards. Of course it's going to get freaked and balk sometimes. As it trains more in that level it will get better at it.

In reality it's a performance number compared to a success number, but it's not exactly random.