The same thing happened to me. I fixed it by getting an API key from here:
https://code.google.com/apis/loader/signup.html
Then you’ll need to add the key to your plugin. Open amazon_affiliate_link_localizer.php in the wordpress plugin editor, and look for the line that has this javascript bit:
<script type=\"text/javascript\" src=\"https://www.google.com/jsapi\">
right after the jsapi add
?key=
and then your API key that you got from Google.
So that line should look like:
<script type=\"text/javascript\" src=\"https://www.google.com/jsapi?key=YOUR_BIG_LONG_API_KEY_FROM_GOOGLE\">
After I did that, my link localization worked perfectly.