We submit our payroll to a payroll company. I have been asked on numerous occasions to not take federal and state taxes out for an employee for a specified pay period. Our software allows us to do this, but I do not know if it is lawful. Is it okay to not deduct taxes once or twice a year?

Is it OK not to withhold... NO! You have to deduct according to the last tax form on file. In order to have no withholding they will have to submit new tax forms.