Answer is fairly simple, the grip. When you hit a draw shot with a firm stroke, the tendency is to over tighten the grip hand. Kind of a reflex action. Once your follow through reaches the end of it's range, the tight grip lifts the cue out of the bridge hand.
If you practice drawing with a smooth follow through, level cue and keep the grip hand relaxed throughout the stroke, the problem should go away.
I highly recommend watching Wu Chia Ching play. Won the WPC at age sixteen using the open bridge for every shot but off the rail/break. His cue never leaves his open bridge. Pei Wei Chang made it to the WPC finals against Pagulayan and he lifts the cue for every shot.
Edit: IMHO, the reason most people struggle with the open bridge is they don't believe it's secure and they get tense/nervous on shots where they have to use a firm stroke. When you get over this fear, you can really start to open your game up. People fear what they don't know or can't trust. If you tackle your fears, they'll become strengths.