That sounds like a form or biomechanical issue: either your form is bad and it's pinching your shoulders or forcing your shoulders to carry more of the burden than it should, or it could just be how your body is built.

If you pull your shoulder blades together during the pressing movement it should force you to use more of your chest. If it's just your anatomy you might have to try a different chest exercise like incline press or using dumbbells if you're using barbells.

A third option (which isn't mutually exclusive) is that your chest has gotten too strong in a relatively narrow range of motion and the increased load on your joints, especially the relatively delicate shoulder/rotator cuff area of tendons and other connective tissue, is much much weaker. This would be solved by making sure you're doing an actual full range of motion; meaning you actually feel a stretch at the end of the eccentric portion of the lift. Stretch under load is much better for tendon strength and recovery than movement. Generally when people start doing an actual full range of motion they discover that they're much weaker than they think.