Embodiments of the present invention provide for continuity of “stateful” routing sessions in the presence of source network address translation (NAT). Specifically, a stateful routing session may be moved from one routing path to another routing path, e.g., due to a routing change in the communication network, where the routing paths have different source NAT status. For example, the stateful routing session may be moved from a path having no source NAT to a path having source NAT, from a path having source NAT to a path having no source NAT, or from paths having different source network address translations. When a stateful routing session is moved from an existing routing path to a new routing path, the routers detect the routing change based on the change in source NAT status using a special link monitoring protocol. Upon detecting the change in source NAT status, session metadata is included in at least the first packet forwarded following detection of the change in source NAT status so that the stateful routing session can continue without interruption.