There are two possible causes for this issue:
1) There is a typo in your MWS credentials. Please double check the MWS settings on your settings page and make sure they are entered correctly. Also double check that the credentials you are adding are indeed the proper credentials. Amazon MWS is not the same as your general Amazon seller account's credentials.
See this video to double check your process: https://joelister.zendesk.com/hc/en-us/articles/205391137-Connecting-your-Amazon-and-eBay-accounts
2) Our system cannot get authorized despite proper credentials. This happens rarely, but on occasion we have found that users cannot sync their Amazon data despite proper credentials. The solution we have found to be most reliable is to have you contact Amazon support and ask that your MWS "secret key" be reset.
Once the MWS secret key is reset, re-input the field with the new key and you should be good to go. After saving MWS settings, you might want to give the blue "Update Inventory" button a press as well. To make sure your inventory will be pulled.
The most common cause: You may have entered the wrong Seller ID- it should be a long string of letters, and NOT the name of your store or eBay username. You should be able to find it where you found the rest of your Amazon credentials.