The simplest solution for this could be to store the files and events as they are created to a central logging server. Something like an Elastic or Elasticsearch, Logstash, and Kibana cluster, or a commercial service such as Loggly.
With the logs centrally managed, essential if you are running a cluster, any issues can be monitored and diagnosed from the logs, and are kept even after the server has been destroyed.
Building an ELK server cluster is simplified due to free open source puppet modules available from Elastic. These will need some customisation for your setup. In addition another module is required on the servers to send their logs. This is via LogStash, also available from the same location.
Summary
Immutable servers work great when used in combination with the cloud, centralised logging and an active update and patching schedule.
Any questions or how I might be able to help you and your organisation, just let me know in the comments below or contact via my contact page.