Yes, if you are connecting to the third-party server over TCP port 25, there is a limit imposed by the EC2 infrastructure, as an anti-spam measure.
You can request that this restriction be lifted, or, the simplest and arguably most correct solution, connect to the server on port 587 (SMTP-MSA) instead of 25 (SMTP-MTA). (The third party mail server should support it unless they really haven't been paying attention for several years.)
See http://en.m.wikipedia.org/wiki/Simple_Mail_Transfer_Protocol
Or, using SSL would be even better.
If you aren't connecting to the 3rd party server on port 25, then there's absolutely no limit.
https://aws-portal.amazon.com/gp/aws/html-forms-controller/contactus/ec2-email-limit-rdns-request ... is the form you can use if you want to request removal of the port 25 block, but this also requires you to establish reverse dns to take additional responsibility for the removed restriction on port 25, if you want to take that route, instead.
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