It sounds like an acquired bad habit, but I would also check the state of his teeth and mouth in general, before maybe changing to a different snaffle. Sharp molars, wolf teeth, uneven bite may all be reasons for this, specially if it wasn't an issue before
You could try changing the bit but I used to have the same problem and it was because the horse was getting away with it because you allowed it and has now turned into a bad habit. What I would do is as soon as they start doing that tell them no, then make them go more forward, with impulsion and then half halt. Repeat this every time they do it. If this doesn't work I'd talk to your trainer or a trainer and see what they say!