Mode. This keeps the router from disconnecting after 10 minutes of inactivity. Log system messages to the router’s buffer or a syslog server Capturing errors and events on a router and ...

Just a suggestion, but have you looked at syslog-ng? It just replaces your normal syslog but to me it seems easier to configure how it handles all the different incoming messages.

Instead, the accepted alternative to Telnet's lack of security is Secure Shell (SSH). Learn how to configure SSH on your Cisco router. David Davis has the details.