Well....welcome to HF
When I am having this issue with my horse I push my hands forward and use my core to lift and push him up into the bridle. I sometimes need to use a bit of shoulderfore to help supple and get him engaging from behind up into my hand and into the bridle more.
It is important to remember to check your position when the horse drops behind the vert! What is your body alignment doing. Fix anything there and then go to the horses body alignment....fix things there
It is also very important to Release when the horse reaches into the contact. This is the reward.....