I would say on a score in the low 600's could possibly qualify for a VA Loan. Being that a low 600 credit score is about the minimum typically the VA will allow, they will want to make sure all other aspects of your file are pretty strong. For example, reserves in the bank (one to two months of PITI), lower debt to income ratios, and good residuals. The lower the credit scores, the more conservative the Underwriter will be when he looks at your file. The higher the credit scores, the more lenient he will be when approving your file.
There is a more than just a credit score that a Lender or VA will look at to qualify a veteran. I have qualified many veterans in the past with low 600 credit scores. It is all case by case, but I would definitely pursue trying to get approved for a VA loan. A VA loan is definitely the best 100% program out there right now, and in alot of cases the only option for most these days.
Raymond....I am very surprised to hear that you were not able to get military buyers with 730 credit scores approved for financing over 95%. When you say military investors, are those buyers buying rental properties, or primary residences? A 730 credit score is a very solid score and they should not have a problem getting approved for a loan at 100% when buying their primary residence. Now Navy Federal Credit Union is a bank or credit union and they will service that loan for the long haul, and if they have chosen as a credit union to not do loans over 95% regardless of the credit score, then that is an internal guideline, but a mortgage bank that sells their loans to other big investors, will do 100% all day for a veteran with a 730 credit score as long as they meet the other standard guidelines of the VA.