Intel(R) doesn't have a built-in way to do what you're talking about. However, assuming you're using Windows*, you can create a script that utilizes WMI to change the "primary" adapter upon ping failure.
You create a script that that pings the remote server through the primary adapter (Adapter A). If the ping fails to return after X number of attempts then, using WMI, it changes the the primary adapter to Adapter B. Adapter B then takes over communications.
I'm not a WMI expert, but I know that it can be used to enable/disable adapters, change link speed/duplex, and configure teaming settings. Take a look at the Intel WMI document located here:
Hopefully that helps some.