As Tonje pointed out, sellers may choose the offer they want to accept. My understanding is that the only criteria they cannot use in making this choice is discrimination against protected classes. However, they can choose an all cash offer of $100,000 over a 100% financing offer of $200,000 if they like, and that is not discrimination, that is choice. (For legal questions about discrimination you should contact an attorney.)
Perhaps if you understood the reasoning behind banks shying away from FHA/VA loans, you would see why some properties would not even qualify for this type of financing. FHA appraisers must not only give an opinion of value on the property, they must also inspect to insure there are no health or safety issues. Any items they spell out as health and safety issues must be corrected before the loan will fund. So if the heating system is not working, that is a health and safety issue and must be repaired. If there is peeling paint on a pre-1978 home, this might uncover lead based paint and is a health and safety issue and must be repaired. (If you would like to speak with an FHA approved appraiser about the home you like, contact me off line through my profile. I can provide you with a referral or two.)
This is a total 'Catch 22'. The bank won't make the repairs and you should not make the repairs. Imagine going into a home you want to purchase and installing a new forced air heating system in responses to a needed repair spelled out in the appraisal. Then for some reason, you don't end up buying the home. You have now INVESTED THOUSANDS OF DOLLARS in SOMEONE ELSES HOME. You probably wouldn't do it for your neighbor, why would you do it for a total stranger. So if the bank suspects that there might be health and safety issues that would require repairs, and they are selling the house AS-IS, the loan will never fund and they are back looking for a new buyer.
Hope that helps you understand the bank's position. Please know that not all banks take this attitude, especially if the home is in reasonably good shape. I have had FHA loan offers accepted on REOs and closed, with very happy clients. It is a case by case basis, so don't give up. Keep looking for your new home and Dare to Dream.
Real Estate Consultant
RE/MAX Palos Verdes Realty