Without have ever seen you hurdle, I can only think of what my athletes do between the hurdles that causes them to faulter.
Some common errors are:
Being too close to the hurdle
Breaking of the hips
Not leading with the knee (long leg swing)
Hurdle clearance is too high
These are a lot of the things I work on with my athletes. A good way to get the rhythm of the 3 step pattern is to stretch the hurdles out about 7-9 feet and run a 5 step pattern. The longer distance lets you focus on running in between and lets you keep the pace of the race.
Bottom Line: Hurdle, hurdle, hurdle. Good luck.