Some people do just seem to disappear. My cousin finally found our great grandmother by searching the census in the location she was supposed to be in page by page. She had been taken in by an Aunt when her parents were both gone. What we know her as turned out to be her middle name...at least in the census. That's a long and arduous process and is not recommended unless all other searches have failed.

The SSDI (Social Security Death Index) will indicate for either parent if SS benefits were requested by either. It will give the death date. Always send off for a copy of the official record, if you can. There may be other clues on them.

If you have a birth date and place for your father...that, with his mother's maiden name might get you a birth certificate from the state where he was born. You may also be able to search for marriage records for his mother in that location.

And yes, do try to account for misspellings of the surname.

Genealogy is a great treasure hunt sometimes, so don't give up. I thought my grandfather's mother was going to be a dead end. Turns out she was a cousin once removed of a US President. But I don't jump up and down about it...he wasn't that great.

Good luck.