By pushing the horse harder to create the feeling you want, lactic acid builds up in their muscles and fatigue sets in pretty quickly as the horse is obviously struggling with the movement. You haven't got long before that fatigue starts to hinder performance so you need make sure you work with intent and efficiency in that short period that you decide to push them harder.
If you immediately come up with an exercise that will help fix the problem you're having, then its best to use that exercise as accurately as possible with extreme concentration on one thing you want to achieve, not six things that you decide need to be better right at that moment. It is better to achieve one prioritised thing in that short period of intense work than to try and address too many things for the horse to cope with, resulting in a tired yet unlearned horse. If you don't have an immediate solution to what is happening, instead of tiring the horse out while you rack your brain for what to do, just take a walk break, clear your mind and then start again when you have a plan.
If our ego starts to take over and we want to achieve an advanced movement with a horse that isn't ready, then the heavy work that is involved in that causes micro-tears in the muscles because they don't have sufficient strength to deal with that work yet. The micro-tears can form scar-tissue in the muscle and become extremely tight, and very difficult get rid of with a normal stretch routine. This is how horses end up tight and locked up, and need massage or physiotherapist attention to work out all the knots. Sure it isn't the end of the world, but it does slow down your overall progress - slow and steady wins the race!
The best way to achieve advanced movements is to keep working on basics and foundations and build up slowly from there, when the horse lets you know it is ready. If you truly listen to your horse, you will be able to feel when he is ready for anything more advanced because his muscles will be sufficiently strong enough.
A problem that creeps in when we decide to push harder is that us as riders also start to fatigue. We can't seem to use our leg as strong, stay upright and strong with our upper bodies, and we compromise our position in order to make the horse move the way we want it to because our neutral riding position just won't cut it in terms of needing the strength to make the change. When we start to feel compromised it is always best to stop and take a breather. I really struggle to understand how anybody expects the horse to do the work sufficiently if not even the rider is able to keep strong and composed on its behalf. A floppy, uncontrolled rider will only throw the horse more off balance and create stress and tension in his mind, again causing muscles to tighten as a panic response.
In every session always try to put yourself in your horse's shoes and try to imagine what he could be feeling by the little signals he is giving you. Horses are very transparent, we just sometimes end up looking straight through it in order to find something more. Ride what you feel, push when you feel the ability is there and rest when the quality of work decreases.