For security reasons, Amazon sets an expiry date against all authorized apps which causes them to stop working after a fixed period of time.
To ensure your Brightpearl account does not get disconnected, you will need to reauthorize with Amazon periodically.
To do so, go to your Seller Central account > Apps & Services > Manage your apps. You will see a table listing your current connected apps, when they were authorized and when they will expire.
The date in bold at the top is the date the app was authorized, and the date in grey at the bottom is the expiry date.
Simply click Renew Authorization in the "Actions" column to reauthorize the Brightpearl app with Amazon.