when you say they lose the subnetwork name, I assume you mean that the subnetwork name becomes unknown? if you run a trace, does the subnetwork include features or not? Can you post a screenshot of the trace results along with the network attributes for the circuit break? Because I think I know the model you're dealing with, I'll use the fields and values from that model (I apologize for the mix of spanish/english).
In particular the Faces operacion and estado del dispotivo of the Interruptor de circuito of the which is the subnetwork controller of the subnetworks. If the faces operacion is set to Desconocido then the entire subbetwork will become unknown (nombre de subred will become deconocido). Similarly, if the controller or the first line's estado ciclio de vida is Fuera de servicio instead of en servicio then the subnetwork will stop at that feature and the remaining features in the subnetwork will become unknown.
Summary:
If the phasescurrent is set to de-energized, that will cause the subnetwork to be de-energized. You should also check to see if the lifecyclestatus of the circuit breaker or the first line in the subnetwork is set to something other than in-service. I normally also suggest checking the terminal connections between the circuit breaker and line, but because these circuits were previously energized that seems unlikely to be the cause of the issue.
