From what i gather, if you have set the FMC for auto climb, it still will not auto climb This is what i have learned.
EX: Initial alt FL390
your flightplan advises final ALT as say, FL410
You check your flightplan in the FMC, go to the waypoint after 390 that says 410
Type in /410S
If you do this then you do not need to reset you ALT, it will do it automatically Oherwise you need to set manually just before the climb.