It seems like eons ago...winter 1977. I was booked in roomettes CHI-NYP on the Broadway Ltd then the Silver Meteor to West Palm Beach for the holidays. The Broadway got cancelled due to unusually heavy snow. So they booked a slumber coach room for me on the Lakeshore Ltd to NYP as that's all they had left. The plan was I'd be able to catch the Meteor from there, but we arrived NYP about 10PM! They put me up in a nearby Ramada Inn and gave me cash for the cab ride each way. Fortunately, they had another roomette available the next day on the SM. So I arrived in WPB on Christmas day rather than Christmas eve.
Another time, about 9-10 years ago, I was on a late running Empire Builder from SEA to CHI and had a connection to the Capitol Ltd. and then on the NEC to Springfield MA. We were running late enough at La Crosse WI that I knew I'd never make the Cap. Amtrak had an 'agent' board there to help with making connections. By the time I got to him (it was by connecting train number), all he said was I'd have to deal with Amtrak Services in Chicago. We arrived Chicago at 9:20...10 minutes before the Lakeshore Ltd would leave. I've been through CHI hundreds of times, so I ran all the way to the ticket counter, got my ticket changed to the LSL (no rooms left), RAN to the LSL Boston section up front (I just made it) and rode coach to Springfield. My original routing on the Cap via WAS saved over $100, and I never got any refunded money. I was happy to get home the same day as planned, but 4-5 hours earlier than expected.
5-6 years ago, connecting at CHI from the California Zephyr to the Cardinal was in seriously behind due to a rock slide in Colorado that delayed us 4-5 hours. I was surprised the next afternoon when they told us (over the PA) that passengers connecting to the Cardinal should get off at Galesburg and buses would take us to meet the Cardinal in Indianapolis. I got gypped out of a free dinner on the Cardinal as we stopped about 2/3 the way there at an exit with 3-4 adjacent fast food places...out of our pockets. I remember that bus ride specifically as I left my one of my 'earned' CSX Intermodal hats on that bus at 11PM when we got off. Fortunately, we got a free 'peak season' UPS/CSX hat before every holiday season, so it was no big loss.
Then, 2-3 years ago, I was on the southbound Coast Starlight to LAX to catch the Texas Eagle through sleeper (#421) to CHI. We were running late at Chico, so they told everyone with connections to get off at Sacramento. When I got to the ticket counter, the agent said I was supposed to get off at Martinez and changed my ticket for Martinez-Bakersfield and bus to LAX. As the Starlight gets fueled and watered at SAC, I had time to reboard and get back in my roomette until MTZ. As I had never ridden the San Joaquin route, I welcomed the chance to do so. The 2 hour bus to LAX wasn't bad at all, though full. I got gypped out a free lunch on that trip. Such is life.
Lesson learned from experience: Connecting in CHI from the west, take the LSL back home to almost 100% guarantee making the connection.