I don't think that the "normal" business definitions of "profit" and "loss" are applicable to our taxpayer-subsidized passenger rail system. If any of these trains could have been run profitably, we'd still have the private railroads running passenger trains. Of course, in today's business world, even operations that are technically "profitable" get axed by businesses if they don't meet the profit targets set by the management.
The politicians are willing to pay the subsidy to run these "unprofitable" trains because they provide useful mobility benefits to their constituents. In the case of long-distance trains, it provides public transportation service to rural areas that can't even get bus lines to come to their towns, plus it allows for mobility of those who can't fly for medical reasons, etc. Plus, the trains provide economic benefits to the rural communities they serve. It's basically a bit of low grade pork spending, which is no big deal to the politicians, because, in the scheme of a multi-billion dollar Federal budget, a billion and a half for Amtrak (of which only a fraction is for long distance trains) is "rounding error," a drop in the bucket. Thus, this basic support for Amtrak appears to continue through administrations and Congresses controlled by both parties.
However, once you start talking about expanding the system, or getting serious about making passenger rail a larger part of our transportation mix, you start talking about having to spend real money, and the opposition to such "boondoggles" increases, enough to usually kill the proposals, unless they're introduced very carefully, in piecemeal fashion.
This is nothing new in our politics. People in New York thought the Erie Canal was a waste of taxpayers' money, even if, in the end, it allowed New York to surpass Philadelphia as the main city in the country. There was certainly no immediate economic reason to build the first transcontinental railroad, the private sector had to be dragged into doing it by government loans and land grants, sweetened with some good old-fashioned corruption and crookedness. In the end, the country got good value for the money expended, I think they eventually even got the loans paid back (though the guy running Credit Mobilier went into a comfortable retirement with his ill-gotten gains).
The only problem with using taxpayer money is that there are many people if think that any public money spent that's not benefiting them in the short term is a boondoggle. "I live on the east coast. Why are we spending all that money for a naval base at Pearl Harbor?" Aside from that, the real issue isn't whether a given train is "profitable" or not, it's whether it's being run in a way that provides the most benefit, which can mean different things to different people. However, with Amtrak's opaque accounting, it's sometimes hard to figure that out.