The command "show log" seems to be with low details and with no history y default, inside 2960-X.
How to increase the detail level and the history (last 365 days, for exemple) ?
As per my understanding your question is - are you not able to view more logs, when you issue show log ?
is this correct - yes? then yes you won't be able to view the logs, it overwrites,
there are 2 options.
1. Offload your logs to Syslog server and retain the logs as long as you want.
2. second configure logging buffered ( if you looking for 365 days, i do not believe you can get that long, depends on logs it generating on your device)
based on your configuration it will storred the command "logging buffered [ size ] - size depends on your device.
Log messages to an internal bufferon a standalone switch or, in the case of a switch stack, on the stack master. The range is 4096 to 2147483647 bytes. The default buffer size is 4096 bytes.
Note Do not make the buffer size too large because the switch could run out of memory for other tasks. Use the show memory privileged EXEC command to view the free processor memory on the switch. However, this value is the maximum available, and the buffer size should not be set to this amount.