Why not repeat the D.O. pronoun in this instance?

Question

No ________ todo el tiempo a nuestro hijo; necesita espacio.

We can't be watching our son all the time; he needs some space.

(HINT: use modal verb "poder" and the verb "vigilar" for to watch)

podemos estar vigilando

podemos estar vigilandolo

Accepted Answer

Hola Allison
In this instance the repetition of the direct object pronoun is not possible. 
You could say:

No lo podemos estar vigilando todo el tiempo. 
No podemos estar vigilándolo todo el tiempo.

But this is only when the other object pronoun is not mentioned. 
You could also use the two direct objects if you start the sentence with "A nuestro hijo":

A nuestro hijo no lo podemos estar vigilando todo el tiempo.
A nuestro hijo no podemos estar vigilándolo todo el tiempo.

There is a Kwiziq lesson on repetition of direct object pronouns but only when they are pronouns. Have a look at this lesson here.
However we will look into other possibilities with repetition of direct object pronouns, like this case to see if we can extend the content a bit. 
Saludos cordiales 
Inma

Answer

The direct object is not repeated with a pronoun in the same clause, except as Irma noted, when the direct object noun is placed in front of the verb--out of its customary position following the verb.