A method of managing connection requests from an application supported on a client. The client has a modem connectable to at least one server via a dialup computer network. According to the method, a list is maintained of the local Internet Protocol (IP) addresses assigned as modem connections are established to the dialup computer network during a session. The list is preferably in Last In, First Out (LIFO) order and includes a latest IP address as the last entry and one or more stale IP addresses. In response to a connection request associated with a stale IP address, the stale IP address is mapped to the latest IP address. The connection request is then redirected using the latest IP address. Preferably, client supports a proxy server which services the connection request locally if possible to avoid network traffic.