> There was no way I could convince her that it wasn't my fault. Perhaps there was a rigid process in place that disallowed her from helping, even though I'd make it to the second flight on time.

Yeah they generally have the capability to prevent that auto cancellation of your segments (within a certain time frame) but in this case unfortunately they were unwilling or it was too late to catch it.

It's generally to protect revenue because buying A-B-C instead of B-C can be cheaper, and hoards of people used to just segments to save money. So they just assume everyone is trying to cheat them.