Most of my late trains were on the order of an hour or so (maybe up to 2) with obvious reasons (engine failure, hotbox, minor accident, or even just plain weather). A BNSF freight engine dragging the dead (except for HEP) Amtrak is limited to 70 instead of 80, which works out to about an hour late at Fresno either direction even with everything else working perfectly -- F59PHI death was at Bakersfield in the morning but they worked the BNSF back to Bakersfield on the late SJ from Oakland so I got it both ways that day.

But the winner was one I wasn't on - just peripheral to. Returning to Fresno from Sac on the late (1830ish) SJ (bus to Stockton), the Zephyr crept in just before we left, and a bunch of empty buses came screaming into the station as we got to the driveway. I figured the train was a few hours late as normal -- had seen it turn up 2-3 hours late on other trips too. The extra buses turned up in Stockton a bit after we got there - passengers for LA who were otherwise going to miss the last SJ at Martinez. Turns out talking to some of them that the Z wasn't a few hours late - it was over a DAY late due to equipment failures and floods/detours in the Midwest. SJ took a little extra time to clear Stockton due to the extra load of people & baggage but ended up only a few minutes late in Fresno.