It appears that you are advancing faster than you are learning. I prefer learning the basics well. This may take longer at first, but progress will eventually prove faster and evidence better skill and enjoyment for both rider and horse.
From the description you provide, I picture a rider who is able to stay on the horse but one who is not truly balanced and following the horse's movement. Ideally, a horse should continue in any gait it has taken as long as the rider continues moving with the horse, unless the horse becomes exhausted. What usually happens is that the rider becomes unbalanced and the horse, not wanting the rider to fall off, slows its motion. Alternately, when a rider is not moving with the horse, the horse must use more effort to overcome the immobility of the rider and soon tires of this added effort. In either case, the key is for the rider to remain balanced and move with the horse. So, how is this done?
We must go back to the basic seat. When sitting on a horse, the rider should be aligned: head over shoulders over hips over heels. Think of standing, legs apart, knees slightly bent, and a horse just happens to be between them. Alternately, think of straddling a stool without a back as opposed to sitting in a chair. Your position should not be held by muscular effort but by balance.
Releasing tension in the muscles of the torso allows those muscles to extend. As they extend, the bones of the spine are allowed to stack naturally one above another. The rider's spine takes on natural shock absorbing curves. The rider's bones support the weight rather than the rider's muscles. All this presupposes that the rider's pelvis is vertical.
When the rider's pelvis is vertical, his weight is distributed between the crotch and the seat bones -- a very stable position. If the rider is sitting on his "pockets" as some recommend, his position may be compared to leaning on the back two legs of a chair. He can easily become unbalanced. Falling backwards, he pulls on the reins or tightens the grip of his legs on the horse to keep from falling. Sitting simply on the crotch is even worse.
While the inner thigh, rather than the back of the thigh, should be against the horse, the rider's legs should be relaxed. Releasing the tension in the muscles around the pelvis, including those in the crotch area, allows the seat to sink deeply into the saddle and provides a lower center of gravity. Releasing tension in the muscles around the pelvis and throughout the legs, feet, and toes allows gravity to do its job in pulling the rider's weight downward. The rider's legs wrap around the horse's body with adhesion; there is no need for muscular gripping. The stirrups support the balls of the rider's feet, but the heels sink deeper; there is no need for the rider to "push" his heels down.
The rider now has a very stable seat with a low center of gravity. Because there is no unnecessary tension in the rider's muscles, the rider's body is free to follow the movement of the horse. Since the rider is relaxed, balanced, and moving with the horse, the horse is not required to use as much effort to move. In fact, the horse can move with the same rhythm and length of stride while being free to release tension in its muscles. As the horse's muscles soften, his movements become smoother and easier to ride. Everything becomes easier.
Once this synchronicity is achieved, the horse should continue its movements until the rider cues it to do otherwise. If for any reason, the horse still begins to loose its movement, a slight re-cue from the rider should encourage the horse to continue. This re-cue should be given as the rider feels the horse begin to change from the canter to the trot rather than waiting until the horse has changed. The sooner the rider re-cues, the less effort is required.
I should emphasize that cues should be temporary. Once a change is made, the rider should simply follow the horse's movement. In such a case, a cue can always be given again. If a rider tries to hold a cue, he can only try to increase his effort if the horse falters; the results are seldom good.