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

There are a large number of possible causes, not all directly involving the BigIP. To start with, I would suggest that you take a packet capture on the unit where the healthchecks are failing. All monitor traffic should be sourced from the non floating self-IP of the BigIP (each BigIP handles monitoring independently), which should simplify capturing.

If the problem is not apparent at that point, traffic is not leaving the BigIP, or traffic is leaving the BigIP and being responded to but we're still not marking the pool members up, please open a support case so we can look at the issue in more depth.

Note that in this case, a packet capture, a qkview, and a network diagram would all help with resolution.