First thought that comes to mind is are your stirrups too long? Try shortening them a little to start with a see if that helps you.
From what I've seen in students that lose their stirrups constantly, it is because they are gripping too much with the thigh, knee or calf, rather than allowing their weight to flow down the leg and into the heel. Think of kneeling your weight into the heel, rather than pushing your heels down which often leads to a chair seat.
Take a deep breath in, hold it, and let it slowly out, and invisage your weight sinking down through your legs and seat. Take your thighs and knees off the saddle (by gripping with your thighs/knees you are blocking the horse's ribs and shoulders thus making the movement even harder to sit on), ensure that your toes are pointed forwards and let your calf sink down the horse's sides.
An analogy I was given by my own coach is to imagine your seat and legs as a slab of meat over a rolling pin. Let your legs drape down the horse's sides without gripping onto it's ribs to hold yourself on. Trust your seat, engage your core by thinking of pushing a swing in a park forward under you, and just allow your legs to hang.
Another one is to picture yourself being a foot taller, someone is stretching you out by pulling upwards on your upper body, and downwards on your legs. This helps to relax and straighten the upper body, while encouraging the weight to sink down the calf.
If you are still struggling, ask your trainer to put you on the lunge. Slip your little fingers under the saddle cloth, close your eyes and focus all of your concentration of feeling the way the horse is moving. Concentrate on her rhythm and match it with your rising/posting. It is easier with your eyes closed as you have taken away one of your sense and your brain will automatically sharpen the remaining senses and allow you to really focus on the rhythm. Allow her strides to 'bump' you out of the saddle on the upbeats rather than pushing yourself out of the saddle. Your rises should come no more than 1-2cm from the saddle if you just allow the horse to 'bump' you out, and you will be a much softer, more balanced and effective rider if you can master this.