Sometimes Zabbix agent slow process log files because of some of used functions and logic (agent scans directory for each iteration and send only one line from log file) are not quite good.
Some of information which should help improve performance of log monitoring on Linux systems:
1. opendir sometimes can be slow. We can use getdents directly: http://man7.org/linux/man-pages/man2/getdents.2.html
2. Instead of checking folder every time we can use notify for Linux OSs: http://www.ibm.com/developerworks/linux/library/l-inotify/index.html?ca=drs- and http://en.wikipedia.org/wiki/Inotify
Most of interesting is second point. With it we can wait changes of specified directory instead of scan directory.