This problem is observable in following situation
1. Create a log file.

 # echo abcd > /tmp/logtest/f1

2. Create item "logrt[/tmp/logtest/f1]" and begin monitoring,
string "abcd" registered in history.
3. Stop the agent.

 # service zabbix-agent stop

4. Remove the log file.

 # rm /tmp/logtest/f1

5. Restart the agent.

 # service zabbix-agent start

6. Create new log file.
Any string NOT registerd in history.

 # echo ABCD > /tmp/logtest/f1

7. Append string to the log file.
string "XYZ" registerd in history.

 # echo XYZ >> /tmp/logtest/f1

In step 5, the agent process knows no files exist.
And it find new file at step 6, the file should be NEW.
This file should be read and register string to history.