The code of the plugin is written in a way that (almost) all errors caused during the execution of one or more actions (like the generation of the API key) is reported back to the user, that way he/she can understand why an action failed.
Considering this and that you did not say in your comment what errors were shown after you clicked the big-blue button multiple times, I assume that the problem is originated by something that is out of the control of the plugin, that is why it could not report a message explaining the error (if there was any).
Anyway, you can email us at this address [1] and me or one of my co-workers will generate an API key for your website, you just need to specify in the body of the message the domain name and email address that you want to use to generate the key.
[1] Sucuri Support [email protected]