I've been working on a better Morale mechanic for 5E. I don't like tying the roll to an ability score, unless it's the leader's Charisma. It's still in the works, but the general gist is:
A creature rolls a Moral Check when each of the following happens:
The first time it takes damage from a Vulnrability (or damage that prevents Regeneration)
The first time it's reduced to 50% of Max HP
When it's leader (if any) becomes incapacitated or flees
Each round that the creature's side suffers a casualty without inflicting one (still thinking about this one)
Morale Check - Roll 1d20 vs. DC: 10 (toying with DC: 8)
Modifiers:
-1 for each Ally Incapacitated or Fled
-2 if creatures is wounded, but not down to 50% of max HP
-5 if creature is wounded to 50% of max HP or less
+1 for every 2 enemies Incapacitated or fled (maybe 1:1, not sure)
+ Leader's Charisma Modifier
Disadvantage if Leader is Incapacitated or Fled
Advantage if defending Lair