No, you cannot. This is basically the entire point of the uniquely generated connection key. It prevents connections from being left in an open state that would cause unneeded server load.
Your question doesn't identify what you are trying to accomplish, nor why you would want to maintain an open connection to Walmart. After looking at Celigo's website, I'm still not sure what you are trying to accomplish, but based on the limited information, it appears that you are trying to do something with the Walmart API that it is not intended to do. Connections to the Walmart API should be on a request by request basis, and do not consist of a live connection.
The Walmart API documentation indicates that you should use a uniquely generated authentication key for every request made to the API, so the fact that you are able to keep the connection alive for a full 5 minutes is even beyond what you are supposed to be doing.
What are you trying to accomplish?