Thinking more about this, I’m pretty sure I’ve guessed what the problem is, by figuring our what you’re NOT telling me. I think what you’re NOT telling me is that these IP addresses are on different networks.
This is going to confuse a pile of things, and Asterisk is only one of them. If they’re on different networks you need to change the IP address of the server, and then restart asterisk.
I’d suggest having two interfaces. One on 1.1.1.10 with a default route of 1.1.1.1, and the other (shut down) with the address 2.2.2.20 with a default route of 2.2.2.2. When you want to fail over, shut down asterisk, shut down eth0, and then start up eth1 and start up asterisk.