Hello there,
One solution might be to use back to back SCR's as the switching elements, with phase and voltage detection to decide on the switching action.
As one phase goes low, turn that phase off and turn the other phase on. If done right this might work if the lines dont go down too often in a day.
It would surely be a good idea to test this in a simulator first however to make sure the switching matrix method works ok. There will most likely have to be phase detection to get the switching action correct.
For the switching, perhaps a micro controller or PROM and associated comparators to make the decisions.
If the switching SCR's dont work because of too much phase overlap, you may have to use an alternate means such as a transistor with bridge rectifier. I think you would have to analyze the effect of switching one phase to the other first anyway though, the effect on the load. The load may have to take a brief interruption in power. If that's not a problem, SCR's would work ok.
So the first thing to do is to analyze the effect of switching phases quickly, assuming it is done very fast. If the effects are detrimental to the load, there will have to be a delay introduced to protect the load at least. If the load can tolerate say a couple cycles delay, then there should be no problem producing this kind of device.
The other interesting thing about the three phase system is that phase A is equal to the inverted phase B added to inverted phase C, or phaseA=-(phaseB+phaseC), which means that if your system is guaranteed to have at least two out of three phases good, you can do a clean switchover with little change to the line voltage! The problem is that if two phases go down at the same time this doesnt work. You also need power transformers too though.
If the phase A goes down at the 90 degree point and you switch to either phase B or C, you'll be switching from plus 100 percent to minus 50 percent line voltage, but if say phase B is inverted first (transformer) the switchover will be much cleaner from plus 100 percent to plus 50 percent, which is much better overall. Thus, if a few transformers can be added that might help alot, although they would have to be able to handle the full load power.
Of course another idea that would be switching transient free would be to build an AC to AC converter. It would take in the three phase line voltages and output a single phase line voltage of the same level as either phase. It would be designed to work even if only one phase was up and running (as a single phase to single phase converter would work anyway). That way if one phase or even two phases went down there would be absolutely no change on the output phase, and when the other phase(s) came back on line they would again help to supply the load power. The switchover would be automatic and transient free. The main difference between this and a three phase to single phase converter is that the input filter caps would have to be increased to be able to handle a single phase input, and the rectifier diodes on the input would have to be able to handle the full load current plus a little more as a single phase input would be designed. This would definitely do it and provide a continuous output to the load with no interruption, but it would cost more as the converter would have to be able to handle the full load power.