According to a post on the RPA hotline which I saw after my initial post, National Train Day was started by Amtrak in 2008 and continued each year until about 2015 when it was dropped from Amtrak's official marketing budget. It is still celebrated by a number of organizations but is not apparently recognized by Amtrak.
As far as I can see, it had proven to be much too successful, just like the Pacific Parlour Car and business class on some trains, so it had to be discontinued. More importantly, the funds required for National Train Day celebrations took away from the funds available for management bonuses.