HA pair in VMware v7 update 3 - Should "power on connect" be enabled, or disabled for vlans/network?
I would begin by making sure that on both machines of the cluster all the network interfaces that *should* be up are indeed up.
If that's the case, you have part of your answer: interfaces that are currently down may safely be configured on VMware with "Connect At Power On" disabled.
If you notice some interface that should be up, but is not, it would follow the opposite logic: "Connect At Power On" should be enabled for those.
You can determine the relation between the VM network interface and the F5 interface by checking the MAC address on F5 with "ifconfig", and comparing to the MAC you see on VMware.