i've noticed there are two kinds of rebellions:

1) religon related, which Ithink has to do with piety of a general (higher piety more chance to rebel) is when your general tells you so and quits after you get excommunicatd for a few turns. it happened to two of my generals when I was playing as aggressive dane.

2) random silent rebellion - which can be either general (and all his forces), general alone or forces alone (I even had forces disappear from the castle...go figure). this is I believe related to both your king's authority and your general's loyalty. I took someone's advice and stopped adopting, marrying into generals under 4 loyalty and my generals stopped leaving me. so I guess to improve the rebellion situation, give your king a huge army, make him your top general (since he already probably starts with 5 stars anyway) and do not hire anyone under 4 royalty, even if they're 6 stars.

so far after I've started doing that, I only lost a few normal units here and there, but I'm also trying to limit how far I take my reinforcements