He accrued unlawful presence as of the day his extension request was denied. This overstay is minor if he indeed left shortly afterwards and should not ground in itself for a denial of a new visa.
Once the extension was denied your father was an overstay and his visa was automatically cancelled. The fact that CBP is erroneously letting him use it to re-enter the U.S. Sometimes it can take months or years for the computer to update as it is not uncommon for the issue to appear during a future inspection.
While written by an attorney who is a Florida Bar Certified Specialist in Immigration and Nationality Law, the statements herein should not be construed as legal advice. No attorney/client relationship has been created without a formal consultation with the attorney and the attorney has agreed to accept your case.
I agree with my colleagues.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.