My sample pool is small and I might as well do an actual test tomorrow but ah well: dynasty live-in had two babies with an apartment dweller (Suzy Strummer so the "Drama on the TV" household and their original apartment). Babies are alive and in the relationship panel (culled babies also aren't listed as rich/single/unemployed in the family tree but these have all the info still there), but can't be found and don't age up. ResetSim doesn't work, but if I switch to Suzy's household and make them active, the babies appear and age up instantly. No bueno for a dynasty though.
This attempt is 100% becoming absolute madness without it and will be euthanized and restarted for its own good but I'm not keen on the future of dynasty babies if this is a problem with apartments in general. My other momma was Carolyn Custard and I was keeping an eye on her only for her to become homeless right after giving birth, but her babies aged up correctly.
EDIT: Two sim-weeks of testing in a fresh Bridgeport save gave me more mixed results. Two inactive households had their babies successfully age up to toddlers without disappearing (including the Drama on the TV apartment huzzah!). One had a disappeared baby and I guess this gets back to the question of what happens to it?