Yes, as
@trainman74 pointed out.
In my case, we lost an hour and a half leaving Chicago. We stopped just outside Union Station (and I mean JUST outside - the coaches hadn't even cleared the tunnel). Our engineer spotted a warning light, and we had to wait for a mechanic to check it out.
We were nearly three hours late by the time we pulled into Kansas City. That's normally a very busy fresh air stop, but I was one of the few people to get off the train. It was pretty surreal.
I assumed we'd make up time in Kansas (that train usually has lots of padding and HIGHBALLS across Kansas), but nope. I woke up at my usual time, thinking we were pulling into Dodge City, but we were actually stopped in Hutchinson. By the time we reached Dodge City, I'd showered and been seated for breakfast.
We remained approximately three hours behind for the rest of the trip. As such, we arrived in Barstow around sunrise and pulled into L.A. around 10:45. I remember the time because they were holding the Coast Starlight, which normally leaves at 10:10.