We recently discovered that the NAT Gateway also terminates connections by issuing a RST packet when it receives the next packet for a connection that it believes to have timed out, effectively causing the new request to fail. The previous recommended approach of NATing in VPC was to use NAT instances, which sent FIN packets when the timeout was hit, cleanly closing the connection. That behavior was far better, since it indicated that a new request should re-connect first.

AWS Support indicated that this was a feature of the new NAT Gateways, even though it breaks outbound connections made by popular implementations such as the Requests python library's urllib3 connection pools. This is pretty unfortunate, and has been a roadblock in migrating to the NAT Gateways.