LTM networking issue:

sounds like asymmetrical routing issue. Did you enable "automap" for source address translation for the VIP on the F5? If I am understanding your situation correctly, what is happening is the dst host will be the VIP on the F5, which then gets sent on to the target node on the pool. Without automap, the src IP remains the same, and when the target node replies, it will go directly using default route...causing the asymmetrical routing. When you enable "automap", the source IP gets translated to the self-IP of the F5, hence, the reply from the node will be directed back to the F5.