GTM flags server down when no default pool members are up

I have an LTM virtual server which has an iRule which may can select a pool other than the default pool. If all members of the default pool are unavailable, the virtual server is flagged as unavailable, and this status is passed to the GTM when the "bigip" monitor is used, thus the virtual server is excluded from GTM load balancing.

Can someone propose the best practice way of overcoming this situation please (or at least tell me where my understanding is incorrect :) )?