LTM tries to persist to pool member down

I'd say that it depends on a few factors. The LB_FAILED event, as this article relates:

...is triggered when the BIG-IP LTM is ready to send the request to a pool member and one has not been chosen (the system failed to select a pool or a pool member), is unreachable (when no route to the chosen pool member exists), or the selected pool member is non-responsive (fails to respond to a connection request).

That suggests an inability to communicate with the pool member at lower levels, like the TCP handshake. If you're only disabling the HTTP service, then the box is still technically alive and on the network, and would be accessible at layer 4. I'm curious if you ever trigger the LB_FAILED event when the HTTP service is down? The "Action on Service Down" option in the pool properties, however, suggests monitoring status. So if a monitor marks a pool member down, the Action on Service Down property would take effect and either do nothing (default), drop/reject, or reselect a new pool member. I would recommend at this point to at least try setting the Reselect option and then doing something more aggressive in your monitor.