Healthchecks failing on one unit working on other unit until rebooting the F5 fixes the problem

Unfortunately your engineer in that case is correct. If the problem is no longer happening, root cause becomes very difficult if not impossible. As to the root cause, it can be an ARP issue, it can be that something has gone wrong (though I am unaware of any known issues that would cause this), it can be that a firewall is blocking an over aggressive monitor. There are many things that can cause the system to fail it's health monitors. While root cause may not be possible, a plan of action should this happen again is not only possible, it's advisable.

I would suggest that should this happen again, you start by taking a packet capture on one or more of the failing monitors. Then take a qkview. Note that if you have the luxury of doing so, it may be better to wait to reboot until after an investigation can be completed. If this is configurational or due to a software bug it may continue happening, and without the ability to trace what is happening we may not be able to identify and fix the underlying problem. F5 support should absolutely be able to help you with this.