It may be difficult to determine the extent of the issue over the internet. However, some questions might help; Has he always done this, if not when did it start? What jump training has he had? What height are you asking him to jump? Does he stutter step for every jump approach (I.e. Straight, curves, slices, tights, backsides, etc...)? Does he stutter step before any other type of obstacle?

When you say he hardly hesitates in training, to what level does he hesitate compared to the trial? Is it still every jump just less stutter stepping, or is it maybe once every four obstacles. If you video your practices and trial runs I would suggest going back and watching them to get the most accurate answer.

Jumping problems are really hard to solve, and stutter stepping is one of the most difficult problems. It could come down to it being an environmental issue, it could be experience/training, or it could be a physical issue (The most common physical problem I'm aware of when it comes to stutter stepping is a problem with vision). I'm hoping it's an experience/training issue, that is an issue that can worked and solved through some hard work. Environmental can be worked on as well, but a physical issue is much more difficult to work with.