Why does my baby get fussy when his caregivers leave his sight?

Separation Anxiety. When a baby is 7 to 12 months old, a very important stage in development occurs called "object permanence". What this means is now your baby can remember and recreate images in her mind. She knows you exist even if she does not see you. But when we leave, and since they do not have a sense of time, it is stressful for them as they do not understand we will come back, causing separation anxiety.
Attachment. Babies do not have a sense of "object permanence", meaning they do not understand the object still exists when it is out of sight, it is simply gone. They have a deep attachment to caregivers, so when one leaves the line of sight, they get very fussy and irritated the loved one is "gone", and very happy when they return. Later, they understand they are nearby, and go looking for them.
Normal fears. Remember the baby is totally reliant upon the parents for everything. Apparently the natural instinct for reassurance is sensitive in some babies compared to others. Thus when that comfort is threatened by disappearance of the comforter, babies understandingly become upset. This passes as the babies learn that others can also protect, love and comfort.
Normal. By 6-7 months, many babies will get upset when their loved ones walk away. That's a sign of normal attachment and development.