Can recurring initial payment period be changed after purchase is made?
According to the official documentation


  Recurring process
  
  When an order containing a Recurring product is purchased for the
  first time for the current user, by default the module reacts on
  "Order is paid in full" event, a Recurring entity will be created
  associated with that product for the current order.
  
  On a cron event, the recurring entities with past due dates are
  retrieved and an order is created for each recurring entity associated
  with the recurring product and customer.
  
  Note: When this cron event runs it's the time to trigger the payments
  or use another technique to build a queue of payments.
  
  All this process is driven through Rules so most of it is modifiable


So from reading this, looks like all you gotta do is check the recurring entity that was created for that particular order and see if the due date is 1 month from now or if it's still 1 year from now. If the latter, then edit it and change the due date to 1 month from now.