last may i was set to fly SFO-LAX-LHR in CW but had a bout of food poisoning. that combined with traffic i missed the check in cut off for the first leg to LAX (had bag to check) and after a back and forth with AA/BA they booked me on the non-stop SFO-LHR...which i missed as well due to not getting to the international terminal with enough time. so another call, they booked me next evening SFO-LHR -- no questions asked which shocked me as i was fully expecting to pay several hundred $$$ -- and i was not on a flexible ticket.
i've never had such personal issues, but thats when i knew BA loyalty pays off in the end when you really need it.