On the Traffic Manager Appliance automatic rotation of the Event Log prevents excessive disk use. When the Event Log file grows to 50MB or more, its contents will be archived. The most recent archive is included in the operations on the Event Log page. Earlier files are compressed with the gzip compression method and stored under a name containing the date and a sequential number. These files can be downloaded and deleted via the UI.
If there are multiple members in a cluster, generating a TSR (technical support report) will include event logs (error logs) from multiple machines with the hostname of the members on the file name. Example hostname.txt-20140723.000.gz (file size 1MB to 3MB).