personally i didn't mind Max trying to find his son (he was the father, mommy was evil but the baby was innocent and needed his help) .. also it lasted.. how many episodes? if we want to be honest he really searched him only in one episode (control) but then he realized the mistake he was almost doing when he wasn't using his brain and he basically stopped to search because the price to pay was too high (plain and simple: he couldn't lose Liz. When he realized that he did almost lose her it destroyed him. he had to face that it was a research that could give him no results since he had nothing really useful to use. this doesn't mean that he didn't love the baby.. but he couldn't lose everything for nothing and he didn't want to lose Liz so he got the lesson and never made the same mistake again)
i love that Liz wanted to help him and supported him. It was mature, i can't see another woman doing the same thing in the same situation. I love that she understood him and she understood that he needed her in that moment even if that meant that she was pushing some of her feelings aside (for a while). But the season was balanced for them because at the beginning of the season she was the one helping him then when she was the one who needed help he was there for her and well.. he did everything for her, he even died trying to protect her.

of course the writers could have avoided the baby's storyline because it was sooo soap opera and it will always hurt Max (and Liz because she loves him and she doesn't want him to suffer). he, they, didn't need that too. Their life was already complex and they had already experienced so many bad things.