If you're having trouble connecting to the Amazon API, which is where you are redirected to Amazon and prompted to login, please see if any of the following reasons may apply to you.
A while back, Amazon enforced users to have one email address for their EU accounts and another for their US/CA accounts. In the last few months Amazon allowed you to "join" these two email addresses to be able to access EU and US/CA/MX marketplaces from a single login. Amazon have informed us that whilst this joins accounts for Seller Central it does NOT join accounts for their API. As such please login using the original email you signed up with for that marketplace e.g. if you signed up with firstname.lastname@example.org for EU and email@example.com - when connecting a EU account use firstname.lastname@example.org , and for US use email@example.com.
Amazon's API will only connect when you have at least one Advertising Campaign active. If you have a new account, we would suggest you add one Campaign via Seller Central and then try to connect again.
If the user who is logging in is NOT the main account holder, they may not have permissions to access your PPC. Please ensure the user is either the main account holder or has the correct permissions.