But to address your question... it's likely they feel you threaten their financial stability, however unreasonable it may feel to you. You didn't mention having any savings or additional liquid assets. Some co-ops in Manhattan require as much as 2 years of maintenance and your monthly mortgage payment in liquidity. Basically, if you lose your job or become disabled, they want to know you can still pay your mortgage and the maintenance.
Unlike many coops and condos, yes, we have had success with VA loans. Yes, we have affordable housing for people with a steady income like yours. And yes, we can work with you to find lenders who will help in covering the remainder of a payment on affordable housing coops.
Please visit our website, and come to a new homebuyer seminar. You sound like an ideal buyer for an HDFC.