You did not indicate that you have tried any of the items that I mentioned to find him. You mention that he was military. If he was not found in the draft registration cards, he may already have been in the military before the registration, but should still be found in VA records.
Here is one more thought.
While not widely known, you CAN ask the census bureau for the family entry in the 1940 census (which might help you) if you meet their requirements:
You must bea descendant.
You must know the exact address at which they lived in that census.