When the web connector says authentication failed, click the blue link beneath the message. Look at the contents:
If you see a message saying trial expiration, make a purchase or contact us for a trial extension request.
Ordering Solution is Unavailable
Check your website and make sure it is running. In this WooCommerce example, the website was in maintenance mode.
Systems like Amazon and ShipStation only allow syncing so many orders at once. If your log says the connection has been throttled, wait five minutes and try again.