Have you configured the Log Level in the Environment’s configuration within the Cloud Portal? From your message above it sounds like you have set the log level when you create the log messages in your app, and you have the appropriate log level filter selected in the Live log viewer, but you may not have configured the log level in your production environment’s configuration.
To do this, go to the Environments page in Developer Portal / Cloud Portal for your app, select Details for your Production environment, and then select the Log Levels tab. There, check that the appropriate nodes have a log level of INFO configured based on what you want to debug, or just use the ‘Set all to Info’ button to easily set all nodes to log at Info level. You will notice this configuration gives you very fine grained control over the amount of logging your app will produce in each of your deployment environments. This allows you to limit logging to just what you need, minimizing any performance overhead caused by logging, and keeping logging output more manageable.
Hope this helps,