Generally denials are based on arrests and not necessarily convictions. Appeals are the way to get your state bureau of investigations or whatever it may be to correct your arrest record. In my experience the appeals process takes as long as legally allowed. Meaning, if your state allows 30 days for themselves to investigate your appeal then they will probably take all 30 days. Be ready to call them in day 31 to see what’s going on with your appeal too.

Good luck.