AW,
There are a few factors that influence the decision to run one vs. two locomotives. Certainly one of the first is quite simply should one fail, at least you can keep the train limping along. I was once on the Silver Palm from Florida back to NY when the head end power failed somewhere in North Carolina. I could actually see the smoke pouring out of the engine for a few minutes.
This left us without power for almost an hour and it did start to get quite warm in the train. Thankfully at our next stop the engineer was able to walk back to the second engine and turn on its generator. This way we were able to get power back for the rest of the trip. Without that second engine we would have had no A/C, no power, no food, and no toilets all the way to DC.
So having a second engine IMHO on a long distance train is a good thing for this reason alone.
The other thing that influences the engine count is how many cars are on the train. Now that Express Service is being discontinued Amtrak is finding that one engine can now haul the remaining cars on many of its trains. So in an effort to hold down costs they are cutting back on that extra engine. It's becoming a cost vs. a potential passenger comfort issue.
Now for something like the Builder, I can see running one engine on each leg of the split. However IMHO east of Spokane it should always run with two. A train stranded on one of the split legs isn't too far from help. A train stranded in the middle of Montana due to engine failure is a long ways from help.
As for the chances, well that's anybody's guess. It really depends on too many factors. Age of the unit, maintenance on the unit, weather conditions, track conditions, even the load that the engine is pulling along with the grade can affect performance. However I would not be at all surprised to be reading at least one story before the summer is over, talking about a stranded Texas Eagle.