You need to grant M2E Pro access to your Amazon account to maintain the inventory and order synchronization with Amazon marketplace.
In your M2E Pro, go to Amazon > Configuration > Accounts > Edit Account > General and click Get Access Data. After you are redirected to the Amazon website, sign in to your seller account and grant Extension an access token. After the token is obtained, please Save your Account Configuration in M2E Pro.
If the error persists, navigate in your Seller Central: Settings > User Permissions > Visit Manage Your Apps, click Disable next to M2E Pro. Then, go back to the Module and Get Access Data anew.