Minecraft – How to prevent villager children from disappearing

The baby zombie you cured before was a baby villager zombie. Normal baby zombies can't be cured.

Here are two adorable baby zombies, one a villager and one a non-villager. I've hit them with a weakness potion and offered them both cookies golden apples. Only the baby villager zombie accepted the apple, as you can see by the dark red spirals around that one compared to the black spirals around the one on the right:

While I was writing this answer up, Harold (the baby villager zombie) had a complete recovery and is now ready to grow up and become a productive member of testificate society:

Technical details

The NBT data for zombies contains two relevant flags: IsBaby and IsVillager. A baby villager zombie is exactly like a normal baby zombie except that it has IsVillager: true while the normal baby zombie has IsVillager: false.

Since the code for curing tests for IsVillager: true, the curing code is skipped if you try to cure a zombie that has IsVillager: false. This makes normal baby zombies incurable.

Where did the baby villager zombie come from?

It's commonly believed that baby villager zombies can only be created by a zombie killing a baby villager. I thought so myself, but this is apparently not true!

Digging through the decompiled game code provided by MCP, this is the line that controls what kind of zombie spawns:

par1EntityLivingData1 = new EntityZombieGroupData(this, this.worldObj.rand.nextFloat() < 0.05F, this.worldObj.rand.nextFloat() < 0.05F, (EntityZombieINNER1)null);

Notice the two calls to rand.nextFloat() < 0.05F. Those are what ultimately set IsBaby and IsVillager. The first call sets IsBaby true in 5% of zombies, while the second call sets IsVillager true in 5% of zombies. Notice that neither depends on the other.

The spawning probabilities in combination:

                   | Non-baby |    Baby
                   |   (95%)  |    (5%)
-------------------+----------+---------+
Non-villager (95%) |  90.25%  |   4.75% |
-------------------+----------+---------+
Villager     ( 5%) |   4.75%  |   0.25% |
-------------------+----------+---------+

So in summary, the chance of a zombie spawning for each type is:

Zombie type      Spawn chance (%)
-----------------------------
Normal            90.25
Baby               4.75
Villager           4.75
Baby Villager      0.25

Your baby villager zombie was likely a very rare 0.25% zombie spawn. You were very lucky to find it and catch it!

One of you said that the max career level is 4, so I used this command

/summon Villager ~ ~1 ~ {Profession:0,Career:2,CareerLevel:4,Offers:{Recipes:[{rewardExp:0b,maxUses:2147483647,uses:0,buy:{id:double_plant,Count:8,tag:{display:{Name:"Coin"}}},sell:{id:wooden_sword,Count:1,tag:{Unbreakable:1,display:{Name:"Sturdy Stick"}}}},{rewardExp:0b,maxUses:2147483647,uses:0,buy:{id:double_plant,Count:12,tag:{display:{Name:"Coin"}}},sell:{id:golden_sword,Count:1,tag:{AttributeModifiers:[{AttributeName:"generic.movementSpeed",Name:"generic.movementSpeed",Amount:-.10,Operation:1,UUIDLeast:112181,UUIDMost:524106}],Unbreakable:1,ench:[{id:16,lvl:1}]}}},{rewardExp:0b,maxUses:2147483647,uses:0,buy:{id:double_plant,Count:2,tag:{display:{Name:"Coin"}}},sell:{id:leather,Count:1}}]},Attributes:[{Name:generic.movementSpeed,Base:0}],PersistenceRequired:1,ActiveEffects:[{Id:10,Amplifier:50,Duration:133333333333320,ShowParticles:0b},{Id:21,Amplifier:60,Duration:1333333333333333200}]} 

and set the career level at 4, this spawns a villager with a career level of 4 that will trade sunflowers named Coin for certain items. Now I tested this multiple times to make sure I was correct, and I was, setting the career level at 4 will prevent new trades from appearing. I am not sure if this works in 1.9, 1.10 or 1.11 because I still play in 1.8.9.