https://aws.amazon.com/solutions/case-studies/slack/
The API isn't even returning valid error codes.
logging error: {"subtype":"api_call_error","message":"{\"ok\":false,\"error\":\"_http_error\",\"status\":0,\"retry_after\":null}","stack":"Error\n
As you can hit their api servers I am betting some replication error in mysql but that is just a guess based on that case study.I am betting they are saying 'connectivity' because that is the error the client logs.