Stop thinking about "Pushing heels down" and replace that thought with "Weight In My Heels"
You have to remember that our heels must beable to do their job, which is be our anchors - they are the anchors that keep us stabalized in our tack. In order to do so, we must allow the weight in our bodies, to naturally dispurse into to the lowest point - which is our heels. But for that to happen, we must ensure that we are not blocking that flow from occuring. No pinching, no blocking with our limbs.
The moment you pinch, grip and block that weight flow from happening - the result you are experiencing happens. Which is, you losing your iron, feeling unbalanced, etc, etc.
So, when you are riding - focus on what your legs are doing.
Work on your two point, get your legs under you, balance over your feet and feel the weight flow into your heels. The moment you lose that, your griping or pinching somewhere and you'll have to put your body back into check.
When you are cantering, and you are losing your iron you are unbalanced somewhere - which causes you to feel you have to hold on with your lower legs. So I would also work on the lune line, with no reins with someone like your coach or someone who is experienced enough to aid you.
The weight flow has to go from your head, into your seat, from your seat into your heels.
Balance, no gripping, weight into heels.
This doesn't mean your heels have to be really low, just so long as your weight is going into them. The moment you feel you are losing your irons - open your legs up *knees off of irons, legs off of horses side* and allow your weight flow to open up again and to follow its path, then allow your legs to go back to where they belong - even pressure from thigh, to knee, to calf.
I hope that makes sense.