Is the horse young? He is using it as a bit of a dummy? Bodey does this if he is a little unsure or getting tired. I have been told its nothing to worry about.
Could be a symptom of gastric ulcers. My ex-racer used to do it when I got him off the track. He has been out 24/7 since I got him, so access to forage all day promotes healthy gut action & he doesn't do it anymore. It would be evident when being exercised if this is the reason.
i dont know if the bit has been the same i used to have a french link snaffle and my mare used to mess around with it and wang her head put her in a french link dutch gag(bit extrem i know) but she is more relaxed and stands up better