From another thread with the same question:
After testing everything I could possibly think to look at, I did some research - it appears that the "API Key can not be blank" error comes directly from the MailChimp API server and has nothing to do with the code in the plugin. It seems to be a common issue with MailChimp extensions for WP, Joomla, and more. Unfortunately, that also means that I have no way of fixing it.
It seems to be completely random whether this problem will occur, with different results for different keys. My searches have found that a lot of other MailChimp extensions from third parties have the same issue.