'Angela must have been neglected for any signs of approaching psychosis not to be picked up.'
Have no idea why 'pick up' is used here.
There's an expression "to pick up on" which means "to notice."
"Did you notice that Darryll was not wearing his wedding ring?"
"NO! I never picked up on that!"
"One thing I picked up on is that the teacher dislikes sloppy-looking work."
pick up on - Idioms - by the Free Dictionary, Thesaurus and Encyclopedia.
So the sentence is saying that it was neglectful that no one picked up on Angela's early symptoms. Her symptoms were not picked up by anyone.
This also ties into the term for detecting a blip on a radar screen (and similar detection events.) This is called "picking up" and it means "catching" in the sense of "catching on to something."
"Lieutenant! I'm picking up a bogey at 9 o'clock!"
The detective felt he had picked up very few clues at the site of the arson.
"Have you picked up any sign of the moon rocket yet?"
"We drove so far out in the country that the only thing we could pick up on the radio was farm reports."
4. Fig. to learn something.
- I pick languages up easily.
- I picked up a lot of knowledge about music from my brother.
7. Fig. to receive radio signals; to bring something into view.
- I can just pick it up with a powerful telescope.
- I can hardly pick up a signal.
8. Fig. to find a trail or route.
- The dogs finally picked the scent up.
pick up - Idioms - by the Free Dictionary, Thesaurus and Encyclopedia.