There are some searches were you can type the fulll name and birthdate then they will give u names and addresses and u can try and firgure out which one is your father. They might cost money but don't u think it's worth it to find your father?
My suggestion would be to research the last name through the rootsweb genealogy boards. You may find your grandparents, aunts etc.
By the way, at rootsweb.com, there is a social security death search. All you have to do is type in first and last name.
If he is dead, at least it will show up there. Remember, there may be alot of people with the same name.
My guess is that this info is input by (human group or groups as opposed to program or scanner) whose historic listings might NOT be from AS complete a period of time as compared to those listings of the massively-pervasive computer age post-1990. This might mean the listings are from Clerk of Court (like those of Real Estate listings, Birth, Death Records from local communities) or it's possibly from SS admin. themselves. Naughty SS Admin, spank spank! Though, when I looked up my Mom's info from 1967 and my Dad's from 1980 (both in MA), they both showed up.
Here's a casual thought: maybe you might want to consider investigating why your relatives don't show up on the list (call SS Admin, possibly)? This might reveal something useful...like refunds or pay-off of benefits from SS Admin, Fed or State taxes or something equally rewarding? Not sure of statute of limitations, though from '60s or '70s. Just a thought.
Hope that helps.