I am working on flying changes with my 6 y/o as well. Ours get really interesting and are a bit *ahem* "expressive"...
The first things that we need to make sure of it that the horse is comfortable, balanced and collected in true canter AND counter canter and that the horse can easily perform simple changes through the walk to and from true canter. The way I like to think of this is "can I do a simple change at every letter in the arena worth an '8'"? This includes A, C, X, I, D, etc...
When your canter is easily adjustable and well balanced then it is just a matter of getting the change done. You really need to not just let the horse get strung out, get pre-occupied with the change or just cruise along while ignoring your aids. The quality of the canter is number one and the change is number two. While we are teaching, we can forget about the frame, getting the flexion/bend changed at the appropriate time, etc.. YOU however, do not get any slack. Equitation and how you ride the gait must not change and the aid must still be perfect. The more you twist around and exaggerate aids, the more you throw the horse off balance.
It sounds like your horse is just losing engagement. An exercise I use to help this is:
Ride on a diagonal line towards x, let us say that you are on the left lead. Before x, collect the canter and go onto a 6-8m volte, bringing the haunches in slightly while keeping the forehand on the correct volte line. When the canter is well collected, jumping and still with impulsion (!!) ride onto the c-line in a shoulder in, and then continue on your diagonal line in a travers (IE half pass, the quarters don't need to be so far over as to constitute a true half pass). Near to the 3rd-4th track, use your right leg to straighten the horse (so the half pass turns into a leg yeild), count 1-2-3 IN THE AID to the change and think about your right leg to left rein connection (ie think shoulder-fore to the right) and similar to the aid for canter, on three the aid is complete and the horse should change. If not, kick with the LEFT leg, while leaving the right leg - left rein connection alone. The horse should jump through.
Remember -quality of canter! This means you can't lose the collection, impulsion or any of the quality of feeling you get.