Service continuity management in a network

A service is provided to a user of a terminal in a network, comprising a service platform and network equipment including session border controllers. Each of the controllers is capable of communicating with the service platform. At least one given session border controller is capable of routing messages received from the terminal, intended for the service platform. This controller decides that the service platform is not accessible on the basis of an accessibility check (302) and then operates in an autonomous operating mode (303, 310) according to which the controller selects a network equipment separate from the service platform and routes at least one message received from the terminal to said selected network equipment.