You could enable manual resume on the monitor to prevent the pool member from being marked up again:
https://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/LTM_config_guide_943/ltm_monitors.html1215771
Setting the Manual Resume attribute
By default, when a monitor detects that a resource (that is, a node or a pool member) is unavailable, the BIG-IP system marks the resource as down and routes traffic to the next appropriate resource as dictated by the active load balancing method. When the monitor next determines that the resource is available again, the BIG-IP system marks the resource as up and immediately considers the resource to be available for load balancing connection requests. While this process is appropriate for most resources, there are situations where you want to manually designate a resource as available, rather than allow the BIG-IP system to do that automatically. You can manually designate a resource as available by configuring the Manual Resume attribute of the monitor.
For example, consider a monitor that you assigned to a resource to track the availability of an HTML file, index.html, for a web site. During the course of a business day, you decide that you need to restart the system that hosts the web site. The monitor detects the restart action and informs the BIG-IP system that the resource is now unavailable. When the system restarts, the monitor detects that the index.html file is available, and begins sending connection requests to the web site. However, the rest of the web site might not be ready to receive connection requests. Consequently, the BIG-IP system sends connection requests to the web site before the site can respond effectively.
To prevent this problem, you can configure the Manual Resume attribute of the monitor. When you set the Manual Resume attribute to Yes, you ensure that the BIG-IP system considers the resource to be unavailable until you manually enable that resource.
To summarize, if you set the Manual Resume attribute of a monitor to Yes and then associate the monitor with a resource, and the resource subsequently becomes unavailable, the resource remains offline until you manually re-enable it.
Aaron