Keep your heels down and "around" the horse. Don't kick, squeeze instead (while keeping your heels "down and around"). You should also make sure your stirrups are the right length, and not too long. If your stirrups are short enough, yet not too short, you should be able to keep your legs still while pushing your heels down in the right position.
Make sure your stirrups are the correct length and the stirrup treads aren't worn out making them slippy. Also check the grips on your boots. If you have no grip it'll always be more difficult to keep your feet in the stirrups.
You loosing your stirrups most likely will be due to your horse being super lazy than your stirrups length, so... Ideally, you'd try to train your horse to move off your leg so that kicking is never used. Start with asking in the walk (so you dont loose your stirrups or balance) and gently squeeze your calf- or heel if thats easier and ask your pony to trot or walk faster, if they dont react immediately use more force when you ask again (whip/spur), do this until they learn to move off your leg immediately and hopefully a gentle squeeze is all you will ever need! Don't forget to also ask from your seat for the horse to move 'quicker' (eg. rising higher and for longer in the trot). Hope this helps :)
Hi there x you shouldn't be kicking as much as squeezing with your calf. If your horse doesn't listen when you ask him the first time give him a sharp tap with your crop or whip. This is because your horse should know that he must listen when you ask ♥. If this doesn't work there might be a problem with his saddle or he might be lame.