Actually your agent is correct, once the FHA case number is assigned and an FHA appraisal completed and turned over to the lender the appraisal value stays with the property, not the buyer, for 4 months. This is referred to as the validity period. See HUD Mortgagee Letter 2009-30 effective January 1, 2010. It used to be a six month period but was reduced to 4 months with that mortgagee letter. Go to HUD.gov to see all mortgagee letters if you are interested.
Having said the above, it does not affect VA nor conventional loans. Only FHA mortgages. What we do here in that circumstance is market the property for a buyer that can qualify for any other type of mortgage but an FHA mortgage.