What is the age, fitness, and strength level of the horse in question? A youngster still trying to find its feet, or a weak and/or unfit horse, will have trouble in the transitions.
Does the horse do a real, three-beat canter or do you have a "four beat canter" going on? Each is a separate problem.
Is the horse cantering in a collected and balanced fashion or "strung out"? I'd bet the latter as the horse in balance will almost always transition down with no muss or fuss.
If the horse is correctly balanced and collected the "half halt" is your friend. It gives the horse a chance to hold/re-balance itself during the downward transition.
What kind of seat are you riding? If you are in the traditional gaited "chair seat" your horse is likely traveling hollow and the "pace steps" are a normal result of this way of going.
The first thing I'd do to answer these questions is have someone video you riding the horse and doing both upward and downward transitions from all three gaits. Then carefully review the videos noting YOUR position and how YOUR position is influencing the horse. Nine times out of ten problems in movement result from rider action, not horse action. The video will help you put yourself in either the 90% or the 10%.
Be Warned: being video'ed is a real "smug basher." It will quickly demonstrate riding strengths and weaknesses. The lens does not lie. It's usually not an ego booster. But truth is essential if you want to solve the problem.*
Good luck in your project.
*The video might also lead you explore tack selection, adjustment, farrier care, and a number of other subjects.