When can we classify it abandonment? Should there be a specific time, months after the father left his child?

Mostly it is going to depend on circumstance as to when abandonment is something that can be used as a accusation against another. Criminal abandonment is another matter and that would involve placing the child in a possibly dangerous situation.

Any questions on Law need to have enough information in it if you want solid answers.

What state is this happening in?

What are you basing abandonment on ?

First we need a context. What do you you want to classify as abandonment and for what purposes. Next we need a general locale as laws vary by area.

If you are trying to change or remove custody due to not seeing a child for a period that is one thing. If you are trying to get someone criminally charged that is another. A father who left the home leaving the child with the mother has not necessarily committed criminal abandonment. So you really need to define what it is you want to do.

Who did he leave child with ?

Why do you want to classify it abandoment, for what legal purpose?

Is the man and wife married ? So is divorce issues part of the reason ?

If it is just custody and child support, there is no need to classify it as anything.

If there is no child support order in place, often many states do not even see him as owing any money. So

1. Is there a marriage divorce issue?
2. is the father listed on birth certificate?
3. Is there any custody orders in place?
4 Is there any child support order in place?
5. Where is this at?