It would be obvious in the sense that the breaker it's connected to will keep tripping until you locate the failed TVS diode and remove it. If you have more than one TVS Diode on the same power block, you'd have to disconnect one side of each diode, one at a time, and check for continuity thru the diodes until the failed one is found.
The less common failure mode is when the TVS diodes fail to clamp transients voltage spikes any longer, which is why @bmoran4 suggested you may want to periodically replace them. Testing them for this type of failure is a bit more complicated.
