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I understand your concern about persistent vomiting for few weeks.
A stomach virus or "flu" is the most common reason for vomiting however it lasts for 5-10 days and subside by it's own.
Other causes which can cause vomiting in a child are:overeating or stomach upset,Gastroesophageal reflux disease,Peptic ulcer disease,food allergies,certain infections,migraine or meningitis.
Another possibility is of cyclic vomiting syndrome (CVS), Its cause is unknown.The episodes tend to start at about the same time of day, last the same length of time, and present the same symptoms at the same level of intensity.
Any vomiting which persists more than 3 days shouldn't be ignored.
And i also suggest her to undergo further blood work like CBC,ESR,Serum electrolyte,Liver function test, Upper GI scopy,Stool routine examination for further evaluation.
A referral to Gastroenterologist should be considered as well.
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