The problem is observed in the following situation
Case-I (agent restarted)
1. Create a log file.

1. echo abcd > /tmp/logtest/f1
   2. Create item "logrt[/tmp/logtest/f1]" and begin monitoring,
   string "abcd" registered in history.
   3. Stop the agent.
2. service zabbix-agent stop
   4. Update 'mtime' of the log file.
3. touch /tmp/logtest/f1
   5. Restart the agent.
4. service zabbix-agent start
   No string registered in history.
   6. Append string to the log file.
   string "XYZ" registered in history.
5. echo XYZ >> /tmp/logtest/f1

Case-II (agent NOT restarted)
1. Create a log file.

1. echo abcd > /tmp/logtest/f1
   2. Create item "logrt[/tmp/logtest/f1]" and begin monitoring,
   string "abcd" registered in history.
   3. Update ''mtime' of the log file,
   string "abcd" registered again. (This action was reported ZBX-11407.)
2. touch /tmp/logtest/f1
   4. Append string to the log file.
   string "XYZ" registered in history.
3. echo XYZ >> /tmp/logtest/f1