I really think Erik's point earlier about strength being a crucial factor may be central to the problem here. There's actually a third factor—balance—which is bound together with strength issues, because until you develop the necessary balance skills, you can't get your leg high enough to stress the hip flexors in a way that builds strength in them, while at the same time, without the strength, you can't get your leg high enough to learn how to position your body dynamically through the kick so that you stay in balance from beginning to end.
What I've found is that there are certain very useful exercises Shesulsa suggested in a discussion along these lines some time ago: instead of working directly on the kick, work on the chamber, and then go from there with very slow motion kicks to (ultimately) full extension, frozen in place for 10 to 30 seconds. They work like this: you stand facing north, bring the knee of your kicking leg up as high as you can, and, while pivoting on the standing leg till your upper body is just past west, rotate your chambered kicking leg counterclockwise downward so that it winds up parallel to the floor, with your standing foot 180º from the target (as people have suggested). And just stand there, maintaining that position as long as you can, with whatever upper-body movement off the vertical you need to do to stay in comfortable balance. Once you get comfortable doing that, try slowly extending your kicking leg as far as you can so that you can maintain that position indefinitely. Try going a little further each time, till you can maintain that frozen position with nearly full extension (you don't want to go to 100% full extension in any case, especially when there's high impact at the end of the kick).
Do that for a few weeks and you will almost certainly find that your strength, flexibility and balance are all much improved, and your comfortable kicking height has increased in a major way. I've field-tested this kind of exercise with my own students and I think it has markedly improved the kicks of the ones who work on it consistently.