I agree it could be alot of things.Is the horse tall? When I jump our TBs, they are pretty lazy over small jumps and don't really give it their all, mostly because they are so long legged, it is much easier to just be lazy then to jump over something that is more like a giant ground pole. Are the jumps made from light weight pipes? If they are, try using something a little more solid, like 2" thick poles that are much harder to knock down and may cause them to feel the pole hitting their legs so they will learn to pick them up more. Is your horse wearing boots? If so, take the boots off temporarily so that the horse can feel the jump hitting their leg.
To test if it might be a rider issue, try lungeing your horse over a few 18" crossrails and verticles. If he jumps fine without a rider, then we can assume that you are inadvertently giving him some signal that has him jumping like that. Hopefully you can figure out the problem and fix it. It is no fun to ride over jumps that have to be put back together after each take off!! Good luck!
~He knows when you're happy
~He knows when you're comfortable
~And he always knows when you have carrots.