Anyone ever experience this problem while riding?

If you have ruled out any pain issues with tack, teeth or anything that could be causing this behavior, have you thought about trying a tie-down?

We had one that flipped his head constantly and it was not his bit, saddle or teeth. It turned out to be severe allergies.

Most definitely rule out any pain issues. There are so many reasons as to why a horse could be throwing their head. Have you tried lunging the horse fully tacked with thwarting bridle on and a halter underneath to see if she/he is doing it with no rider? The saddle could be pinching, girth too tight, pad rubbing, also try loosening the headstall by a hole. Some horses don't like a tight bit but a looser one. Also are you using a 2-piece or 3-piece or even a chain mouth piece? Nose band? Tie down? If your using a 2-piece try a 3-piece with rollers or just a 3-piece. I own one of the most ridiculously picky sensitive horses out there. Can't use an off brand bit, nor a 2-piece (2-piece have a nut cracker effect and could be hitting them on the roof of their mouth). Also the bit can't be where a normal bit rides as he will throw his head. Do you float once or twice a year. Some horses need twice a year for the speed their teeth grow.
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QHwillow, I'm wondering if your horse was ever taught correctly how to carry a bit and respond to it. You may need to do a lot of groundwork with her, first teaching her to give her head while wearing a halter (side to side), then using a snaffle. To do this face the horse's shoulder about a foot away and begin to bring her nose around to your hip. Don't force it but coax her. If she resists that's ok, just stick with it and she'll gradually do it. Her off side will likely be more resistant and will require more repetitions. You may gain only an inch. Be sure to always let go no matter how far or little she turns her head. Allow her to straighten then begin again. Same with the snaffle. When a horse resists there is tension in the poll and this exercise is to teach her to loosen it. CA refers to it as a one-rein stop. Once she will bend repeat the exercise before you ride then do it from the saddle with your arm out to the side somewhat.