Cannot acess interface management

from your initial post you suggest you installed two BIG-IPs on your workstation. so something like virtual box or VMware player is used? that isn't really a normal / supported setup.

BIG-IP wouldn't block management with default settings, there is a bigger chance the hypervisor or your setup is doing something which causes this. unfortunately that is quite tricky to trouble shoot via a forum.

you could try the VMware or Virtual box console to check if traffic reaches the interface.

also if your management changes with reboot you might be using DHCP, try with fixed IPs for a change?