Board of Education medical requirement for F5 visa- part- time

I have an F visa and took my medical in September this year. I registered with Local Board of Education in October with a Hakwan. I am now trying to register with two other potential employers, but they are saying I must use a medical that is less than a month old. Is this applicable to F visas. Board of Education is insisting I take it again only 2 months later. I will only be part-time.