What happens when a witness you subpoena to testify at your licensing defense hearing does not show up?

A subpoena is used to compel attendance at a hearing, and a subpoena duces tecum is used to compel production of documents at any reasonable time and place or at a hearing.  Subpoenas must comply with CCP §§1 985–1985.4; Government Code, § 11450.20(a).) The subpoena compels attendance or production by a witness who is a resident of the state at the time of service.
The California Administrative Procedure Act (APA) provides subpoena power to all adjudicating state agencies, presiding officers, and attorneys for parties. (See Government Code, §§ 11450.05–11450.50.) It also provides for use of a written notice to attend in lieu of service of the subpoena, as in civil practice. (See Government Code, § 11450.50; Code Civ. Proc., § 1987.) Thus, if a party wants someone to come testify at their hearing, it has the means to issue a subpoena to order them to do so.

But what if they disobey it?

Well, failure to comply with a subpoena may be punished as contempt. (Government Code, § 11450.20(b).) The agency or Administrative Law Judge may seek contempt sanctions by certifying the facts to the local Superior Court and filing an order to show cause. (Government Code, § 11455.20.) If the agency fails to petition the court, the respondent may be able to do so directly. (See Gilbert v. Superior Court (1987) 193 Cal.App.3d 161 (party to APA administrative proceeding may file petition in superior court to enforce administrative subpoena duces tecum, even though pertinent statute provides that agency must certify facts). In Gilbert the court reasoned that the respondents in an administrative proceeding are entitled to petition the superior court to enforce the agency’s mandatory duty to seek subpoena enforcement or to take the shortcut of petitioning the court directly.

But what about my case?

More than likely, you will be able to request a continuance. And so long as you are able to produce evidence of a properly served subpoena, you would have good cause for purposes of obtaining it.