I want to know how long a parent would have to be away from a child to have parental rights signed away?

There is not a time, This would help to know what country, we are international. And if the US what state.

For example, in Georgia, not visiting and not paying support is NOT a reason to lose any rights.

But in general, merely not seeing the child does not make him lose any rights.

Also is he paying any child support, most courts view a payment as a "contact"

What makes you think that parental rights can be signed away? You seem to be laboring on some misconceptions about the law and practical enforcement of it. First, ANY question on law needs to include your general locale as laws vary by area.

However, in the US and most other countries, only a court can terminate parental rights. Courts are VERY reluctant to do so. Especially in a case where the parent is just not exercising those rights.

You may find this sticky helpful: https://www.askmehelpdesk.com/family-law/signing-over-rights-read-first-116098.html

If you want to explain more about your situation, we may be able to help further.