Reckon Accounts can randomly disconnect, the following are ways to try to reconnect.

Close both The Order Exchange and Reckon, check the Task Manager and close any running QB processes.

Open Reckon, go to Single User mode. This can be done by going to File and Switch to Single User Mode, note that you need everyone out from the system.

Go to Edit => Preferences

Then go to Integrated Applications => Company Preferences

Remove the access

Close Reckon and check the Task Manager to close any running QB processes.

Open The Order Exchange. Then on the connection window click  'Test'. You should get a message saying cannot open Reckon automatically. This step seems important as it clears the connection correctly from Reckon

Close The Order Exchange and check the Task Manager to close any running QB processes. 

Reckon (still in Single User Mode)

Open The Order Exchange. On the connection window click  'Test' and you should see the following open in Reckon

Choose "Yes, Always" and set the Login as the Admin account. Also check the "Allow this application to access..." to true.

Click yes to any other questions.

Continue to log in to The Order Exchange (should say connection is fine)

Close The Order Exchange

Switch Reckon to multi-user mode

Open The Order Exchange and the connection should now be good