With every horse I ride, I need time to adjust to their trot.
Sitting trot is not easy. However, so many can do it, why would we not be able?
At first I was allowed to grip with my one arm to the front of the saddle, so I can feel the horses rythm. Plus this was a dressage horse with a wide, bouncy trot. God I hated his trot. I kept sliding around the saddle, tipping forwards and what not.
After a few rounds holding to the saddle, mind you, this is all on a lunge now, i started being able to sit him slightly better. never got to the point of 6 minutes in that trot, but that helped.
Next to help me with sitting trot, I was riding another horse at the same time, that summer. I just took her to the outside small arena, it had a wall, took her away from the gate and did lots of circles both directions, later already full rounds etc. Basically I warmed her up, did a few things with her, and then just kept sitting. She had to listen to me hard too, when I was asking for a lot of transitions etc. I kept losing my stirrups then, starting to grip occasionally, but I think it took me a week straight riding her to get a hold of her trot, and be able to sit for a bit longer. My core still never had the muscles needed for longer sitting trot.
Then I went to another trainer, who just asked me to sit for a bit. I was actually suprised it worked, it was a jumping saddle, new horse, but she had a smooth trot, so I just sat there, and didn't even lose my stirrups!
Now I work with my friends horse.. well.. his trot can be bouncy, I lose my stirrups very rarely, my core is working hard, (Imagine that your waist is a spring, like the one a car has for a wheel, it absorbs the movement), everything else relaxed and legs trying to make him move on. But yet, I notice my legs going a bit forwards too, when I sit more back to be able to sit his trot.
But basically, it can be done, just the best is at least 20 minutes alone in an arena, sit sit sit, repeat, repeat and keep at it. when you get it, you will know.
But of course, doing it once a week does not strengthen your core fast enough. You might wanna look into core exercises off the horse, to strengthen yourself.