It is most likely a socket timeout. Excon tries to use persistent connections when it can, but sometimes this comes back to bite us unfortunately. It appears that mandrill-api is attempting to reuse the same connection/socket in it's call method: https://bitbucket.org/mailchimp/mandrill-api-ruby/src/03e3e28e77dcba31eab7d2f9e2216b5a01d2110d/lib/mandrill.rb?at=master#cl-35
That should normally be fine, but might lead to the behavior you are seeing above if a given session lives for a longer time (ie probably greater than 30 seconds, at a guess). Calling #reset on the excon connection would ensure that you wouldn't encounter this, so that is probably the safest way (though this prevents persistent connections from being used, so there would be a small performance hit if you are doing a lot of requests).
I hope that helps, perhaps we should discuss with mandrill-api about updating this. Might just depend how intermittent (or not) the issue is, given the performance hit involved. Hope that helps, but certainly happy to discuss/help out however I can.