Other posters have already pointed to this, but there are a few points worth expanding on:

1. Passenger rail was probably never profitable. It was only starting in the 50s that railroads developed more sophisticated cost accounting methods that allowed them to pinpoint costs more exactly taking into account factors such as train speeds, train weight, train frequency, and so on. Up to that time, railroads were able to determine directly related costs pretty well, but once they got a handle on the fully allocated costs, most began to push hard to get out of the passenger business. There were some exceptions obviously, not to mention the fact that the corporate culture back then was different, viewing running passenger trains as (a) an obligation that had to be borne in order to protect their freight business and/or (b) necessary to attract and impress freight customers.

2. David P. Morgan wrote a lengthy treatise in Trains magazine (April 1959, if I'm not mistaken) called "Who Shot the Passenger Train?". Although the conclusion was "everybody," Morgan's analysis, boiled down to its simplest level was that passenger rail was a private business operating with privately paid-for infrastructure, and every other mode was private business running on publicly funded infrastructure. This is what is known today as "well, duh."

3. Lyndon Johnson remarked back in 1967 that the government was "not in the business of saving passenger trains" when he signed the legislation taking away the mail contracts, effectively gutting the subsidies that kept a lot of trains running. 3-1/2 years later, we got Amtrak, putting the government squarely into the business Johnson said the government should not be in. IMO, it would have been better to just have the government pay direct subsidies to the railroads and allow them to keep running their own trains. No one can seriously argue that Amtrak runs better trains than UP or Santa Fe did 40 years ago, and I think an argument can be made that even SP's Cascade was a decent operation well into the late 60s.

There's got to be a better way, that's for sure.