Have you tried reaching out to obtain your fathers medical records from the VA system they may have his discharge papers within his records. You can also try talking to your states or fathers state depending were he lived. States have Veterans Service Office and also and the County level as well. Most soldiers like myself recorded their discharges with the county recorder or county clerks office. Might want check those avenues.
Also if it has been sometime since you last requested from NPRC I would recommend doing it again as well, but currently they are only processing "emergency request" for things such as burials, and medical.
When requesting make sure you request his full military/medical records as well.
Dear Ms. Pittard,
Thank you for posting your question to the History Hub!
A staff member checked the NPRC registry and the electronic records system maintained by the Military Service Department using the name and Social Security Number which you provided. They were unable to locate a file for him but did locate some information indicating that a claim for benefits had been made. In many cases this is because the member may have served in the Army National Guard or Reserves.
For access to personnel records of non-active duty Army National Guard enlisted personnel and officers, please contact the Adjutant General of the appropriate state using the addresses listed on the National Guard website at https://www.ngaus.org/states-territories/state-association-directory.
For the location of his Army Reserves records, please contact the U. S. Army Human Resources Command, ATTN: AHRC-PDR-VIB, 1600 Spearhead Division Avenue, Department 420, Fort Knox, KY 40122-5402. The telephone number is 1-888-276-9472; email address is firstname.lastname@example.org; and the web site is www.hrc.army.mil.
We hope this information is helpful.