It happens, and it is frustrating when the record in question is a single misdemeanor from years ago with nothing since. But a denial is not necessarily the end of the road.
The standard background check that every visitor goes through flags criminal records automatically, and some facilities apply those filters broadly. A felony is almost always an automatic disqualification through the standard process. A misdemeanor falls into a grayer area that varies by facility, and some institutions are stricter than others about where they draw the line.
If you were denied, the next step is a direct appeal to the warden's office. Write a letter that is respectful, humble, and focused on the future rather than the past. Do not spend much time on the charge itself or when it occurred. Instead, make the case for why your presence in this inmate's life is a positive force and how you intend to support their successful reentry and rehabilitation. Wardens have the authority to override a standard denial, and they exercise that authority when someone makes a compelling case the right way.
Keep the tone cooperative throughout. You are asking for a favor from someone who has no obligation to grant it, and the approach matters as much as the argument. A letter that comes across as entitled or argumentative closes the door. One that is genuine, forward-looking, and respectful gives you a real chance.
A single misdemeanor possession charge from over two years ago with a clean record since is about as sympathetic a set of facts as these appeals get. Make that case clearly and let the warden decide with full information in front of them.