The problem is your either landing on your wrist when you get tackled which is more a reflex because when you drop to the ground your hand reaches out to stop you from falling, or you might be just palming off to many people in which case you should just strap your wrist and put some deepheat on that should help it
Without knowing what age group or position you play in rugby its a little hard to answer. Are you in the front row ? --- because a lot of pressure is placed on your arms and shoulders. Don't risk a serious injury -- go and see a doctor.