Interestingly, I came looking for a similar question to be answered..

As I understand it and according to the Copa website, you must put the reservation on hold for 48 hours which is an option on Copa site, Then request and complete your booking via phone reservation center or sales office.

* To pay for a reservation booked through copa.com you must select the option “Reserve and hold my itinerary for 48 hours” and then contact our Reservation Center or Sales Offices.

I have two questions:

1. How long can you stay in Panama under the Visit Panama promotion before traveling on to your destination?

2. I know the Visit Panama opportunity is once per itinerary, but can it be used on either the "intial way through" or "return through"

Thought I would check here before calling in case the OP has the answer already.

From the website:

If you want to take this opportunity while travelling through Panama, when you connect at the Hub of the Americas to your final destination, get to know this beautiful country, Copa Airlines and the Panama Tourism Authority can make this happen. This promotion is available for all the destinations Copa Airlines flies to. The baggage allowance for your trip will depend on your point of origin and destination.


To visit Panama, the following conditions apply:

• Make your reservation and purchase your ticket through our Reservation Center, Sales Offices, our web site copa.com* or through your favorite Copa Vacations agency.
  
• The itinerary must be operated by Copa Airlines and/or Copa Airlines Colombia.
  
• Visit Panama only applies prior the purchase of the ticket. Once purchased the ticket or started the trip, the promotion does not apply.
  
• Request to reserve your itinerary with a stop in Panama before completing the purchase of your ticket.
  
• Only one stop in Panama per itinerary is allowed. With this benefit, you will visit 2 destinations for the price of one.
  
• Payment of the departure tax from Panama must be paid at the time of the ticket purchase.
  
• Promotional rates do not apply.

* To pay for a reservation booked through copa.com you must select the option “Reserve and hold my itinerary for 48 hours” and then contact our Reservation Center or Sales Offices.