The author of the text suggests that monitoring key metrics can help keep a Graylog server operational, allowing log data to remain available and accessible. The recommended core metrics include disk IO utilization, available disk space, CPU usage, memory usage, and available file descriptors. Available disk space is considered the most critical metric, as running out of it could lead to serious issues. The author encourages readers to review these metrics and gather them using InfluxDB and the Graylog Telegraf plugin.