@NSou If there are any active messages on the queue/subscription then the service bus function should be triggered continuously until and unless all the messages are not consumed from the service bus entity (queue/subscription). I have tested the same at my end (queue having 4000 existing messages) and couldn't observe the same behaviour as you have mentioned. The function was continuously getting triggered until and unless all messages were not consumed.
Tested using function v3 C# code.
[FunctionName("Function1")]
public static void Run([ServiceBusTrigger("gittest", Connection = "ServiceBusConnection")]string myQueueItem, ILogger log)
{
log.LogInformation($"C# ServiceBus queue trigger function processed message: {myQueueItem}");
}
The output that shows that the function was continuously triggering :
Can you share the code snippet along with the other configuration.