Well, that´s the traits "causing" the additional HP ( and for the AI there could be some hidden ones, too ).
To effectivly kill those "tough and near immortal" generals you need a clean charge on them with a medium/heavy cav. unit, preferably with "ap" lances ( which most are anyway ), once they are in a pitch battle. Use "ap" infantry like axemen, or medium cavalry with axes, to decimate them, or soften them up with your slingers a little bit before an engagement. Hope this helps.