If it's in full sun, that would explain it - they burn too easily, so need to be in light shade, or filtered sun.

Lucy, I think it's a little early for hornbeam leaves to be turning brown from summer heat and sun. This may indicate a root problem, but don't repot now. Next spring, repot the tree and work on the roots. Plant in a more free-draining soil than Brussel's mix. I recommend completely inorganic soil mix with akadama.

My hornbeam is doing quite well this year, even after the freeze that turned all the leaves to brown, slimy mush. I just air layered it and will be posting an article on it as soon as I get roots to show.

Here is a link that might be useful: Sashi-eda Bonsai Weblog