When Daylight Savings Time ends in the United States every November 1st at 2 a.m., Amtrak has to have a solution for the sudden loss of an hour. Its solution is simple–trains operating when the transition occurs simply sit idle for up to an hour until time catches up to the schedule.
When Daylight Savings Time starts again, trains just become one hour late.
It doesn’t seem to be on their website now, but Amtrak used to have a timetable page that summed it up thusly,
Fall and spring time changes
Amtrak operates according to prevailing local time, either standard time or daylight saving time. At the spring time change (second Sunday in March), Amtrak trains traveling overnight will become one hour late and will attempt to make up the time. At the fall time change (first Sunday in November), Amtrak trains traveling overnight will normally hold at the next station after the time change then depart on time. Arizona does not observe daylight saving time. Please observe footnotes in schedules for trains serving Arizona to determine your departure or arrival time.
This is not apparently unique to Amtrak–national passenger railroad systems in other countries that have daylight savings time typically end up doing something similar. Some rail systems apparently cancel any normally schedule trains that would be operating during that hour long window.
The start or end of daylight savings is not an issue for the passenger airline industry because the aviation industry long ago settled on using Coordinated Universal Time (UTC).