Check bulbs. Swap the bulbs around from passenger to driver and see how that works. If it's still persists, I have a feeling that the ballasts may be leaking. I had a similar problem caused by either heavy acceleration or heavy braking, water from the headlight housing shifts inside the ballast causing the bulbs to shut off momentarily. Switching from parking position to "0" or "1" causes it to turn back on but the system goes through the same cycle process and finally shutting off again. If I leave it off for awhile, the problem goes away eventually until I trigger it again. cycle and repeat.
The problem was caused by my headlight condensation, and having water seep into the ballast housing. This problem can also be caused by a weak or worn ballast gaskets.
Don't even bother switching bulbs from side to side. Buy new bulbs, it WILL fix the issue. Mine did the exact same but with left turns. Ballast shouldn't respond to left/right turns, if it were going it would flicker without any conditions.
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Sounds like a loose connection or water sloshing to me as well.
Maybe look at the wiring, and see if there is anything else that may be loose - It may not be the headlamp / ballast wiring itself, maybe something else is loose and presses against the headlamp / ballast wiring when you corner hard. (Try "wiggling" anything that could come into contact with the lamp/ballast wiring.)