Monitor log down and up respectively

Is this issue relate to latency when F5 monitor response packet doesn't comeback in time? Or it just known issue which is benign.

i do not think it is benign. have you tried tcpdump the health monitor traffic?

I had the exact same problem, check F5 support response below.

You can enable or disable debug logging for the bigd process from the BIG-IP command line or from within the Traffic Management Shell (tmsh). Please only do this for a short period of time. This is very verbose and can cause logs to fill up quickly. Logging for extended periods of time may result in disk exhaustion and failover. Bigd log files are not rotated.

To enable debug logging for the bigd process, type the following command: tmsh modify sys db bigd.debug value enable

To disable debug logging for the bigd process, type the following command: tmsh modify sys db bigd.debug value disable

To permanently save the changes to persist through a restart, type the following command: tmsh save sys config

We do not have monitors ( active monitoring or syslog) for nodes or pools. We do have healthcheck so F5 support wants me to monitor by tail -f and use the above debug. Its not at all possible for me if its for you then you can give it a shot or You can always ask their support. Let me know if you get the root cause for this problem.

Check out DEV Central's Troubleshooting LTM Monitors article. https://devcentral.f5.com/wiki/advdesignconfig.TroubleshootingLtmMonitors.ashx