Two scenarios, calls inbound and calls outbound.
For inbound, robust DNS/BGP routing, and SIP proxies that are mutually aware of each other. The Phone Numbers called from outside must resolve to something that will answer them and send to an effective endpoint in the absence of the prime destination, they are rarely under our control apart from rudimentary fail-over provisioning from the VSP, so in your interest have them go to a robust domain that is not dependent on an IP address, that might or might not be available.
For Outbound, redundant networks, properly configured routers that also understand BGP. Have your Asterisk boxes register with the Proxy services, these to be placed strategically depending on your topology. They will be able to call within the range of the currently available network, and can load share and all the good stuff that Asterisk can't, reroute with much greater nimbleness than Asterisk, and are just generally better designed to handle networks that break (they all do of course)
The underlying problem that DUNDI tries to overcome is that Asterisk is a B2BUA (back to back user agent) so it's self knowledge of the network is severely limited, yet until/if it develops to a wider audience DUNDI is also self limiting and needs third party compliance (not yet in most places). thus the need to register with a proxy that is more agnostic, some might argue that DUNDI is in fact such a proxy, others will disagree.
Other solutions E164 (not yet in most places), ENUM, (not yet in most places)
There are other solutions!!