There are some limitations of Authorize.net payment gateway while processing recurring payments:

• You can only select weeks, months and years for Cycle Period.
• The process of placing an order is manual. 

To process next order follow these steps:

1. Login with admin credentials.
2. Go to Administration section.
3. Go to Sales > Recurring Payment, you will find the list of the recurring payments which includes customer, cycle length, cycle period, start date, next payment date, total cycles, remaining cycles etc.
4. Click the Edit link in front of the customer for which you want to place order by checking the next payment date.
5. You will see two tabs Recurring Payment Info and History, click the History tab.
6. Then click Process Next Payment (Create a New order)” button to place order on behalf of that customer. Details about how recurring payment works (http://www.nopcommerce.com/boards/t/13795/authorizenet-recurring-support-manual.aspx)

Details about how recurring payment works here.

NOTE:: nopCommerce already uses ARB API. All recurring payments are automatically processed on Authorize.Net's side. But Authorize.Net does not notify nopCommerce store when a new payment is processed. That's why you have to manually click 'Process Next Payment (Create a New Order)' button in order to create a new order. It just places a new order without any call to Authorize ARB API web service because it's already processed on Authorize.net side.