The -le suffix refers to the baby, and is used along with al to show that la cabeza belongs to the baby. This is a very common way of indicating possession in Spanish, and is the same as saying mantén la cabeza del bebé. If you were translating literally, you might say To the baby, support the head....
Another example of this structure is:
A él le han robado el coche.
'They have stolen his car', or more literally: 'to him, they have stolen the car.'
Mantente la cabeza on the other hand, would suggest that you are supporting your own head, and would be analogous to mantén tu cabeza.
The negation of the statement would be:
No le mantengas la cabeza al bebé con la mano bajo el cuello.