What steps are necessary to identify the cause of this phenomenon?

Explanations:

Ensuring that file permissions for the monitored files allow the CloudWatch Logs agent to read the files is critical. If permissions have been modified and the agent can no longer read the log files, log delivery will stop, leading to gaps in the logs sent to CloudWatch.

Verifying that the OS log rotation rules are compatible with the configuration requirements for the agent is essential. If the log files are rotated without proper configuration in the CloudWatch Logs agent, the agent may not be able to track the new log files correctly, causing a halt in log delivery.

Configuring an Amazon Kinesis producer is not directly relevant to identifying issues with the CloudWatch Logs agent. While Kinesis can be used for log management, it does not address the specific problem of logs stopping delivery after a certain time period in CloudWatch Logs.

Creating a CloudWatch Logs metric to isolate a changing value may help in monitoring logs, but it does not directly identify why the logs stop being delivered. Metrics are for monitoring and alerting, not for troubleshooting the configuration or delivery issues of the CloudWatch Logs agent.

Using AWS CloudFormation to maintain the configuration file for the CloudWatch Logs agent is not necessary for identifying the delivery issue. While it can help in managing resources, it does not contribute directly to understanding why the log delivery stopped after a specific period.