Attempting to recycle errorlog
Means you have run the command sp_cycle_errorlog
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SQL Server is terminating due to 'Stop' request from services manager
Means the SQL Server Services (MSSQLServer and SQLSERVERAGENT services) have been stopped.
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So, the reason your error logs aren't growing larger is that something/someone is stopping them from growing.
Do you have a job that stops the SQL Server services?
Are you or someone else stopping the services?
Since your logs are only growing to 3KB, I would guess that something is stopping your services on a regular basis.
I'm not sure that this will do it, but use Enterprise Manager, drill down to your databases, right click on Master, select Properties, go to the Options tab. Is the database set to AUTO-CLOSE? Check the other databases.
-SQLBill