I don't know if it's already a known issue but I noticed that when I place sims using move in if they have a custom career it disappear, but if I use place a copy from edit town and then I selet the household the custom career remain.

I have never experienced it, but I never use the move in option

Does it also disappear when using MC add sim to the lot?

Don't know. Never used MC to add sims.

If you're using Move In at the very start of a save, before you've ever made it to live mode, the custom careers may not have fully loaded. In that case, the sims would lose their careers in the few seconds between when they're placed and when the careers do load.

The workaround would be to load a different household and play it for a few sim-minutes, then go back to Edit Town and place the sims with custom careers.