Do you find yourself getting nervous in the ring (stage fright?) I know the first time I showed, I was in the dressage ring, and I definitely made an impact on some of our scores, just from being nervous. Things that my horse would normally do just perfectly at home in the arena and in the warm up ring, she was doing terribly with, and it was all because I got really really nervous and tensed up and she could feel it.
Maybe some of it is your nerves rubbing off on your horse? If so, you should feel good that you and your horse have the kind of connection that allows for your feelings to channel through him! But of course, you don't want to have to deal with it in the show ring. If that's it, then time and more shows will definitely help
On the other hand, if HE just gets nervous on his own (which is also possible), maybe he needs something to help him relax? Like Quietex or something like that, starting a few days before the show?