What can cause a child to throw up three to four times a week? She has been doing this for years she is only 4.

Could be reflux. Your child may have gastroesophageal reflux or gerd for short. Gerd is easily treated with watching her diet, not letting her eat too late a dinner just before bed, and sometimes medication is used. But before you conclude this is the reason- she needs to see her doctor- they will get more info from you and decide.