Is there a legal point at which non payment of support = grounds to lose rights?

I have heard something to the effect that there might be a law in MN that syas non-payment of child support obligations for an excessive amount of time (beyond $10,000) may be grounds to file to have the obligator's rights suspended or revoked.
Is there any truth to that?
And if there is not such a law in existance- WHY NOT?! Why isn't financial neglect by the non-custodial parent viewed with the same contempt as say... the custodial parent not bothering to feed, clothe, or house the dependant child(ren)? It seems the court has a very stilted point of view on this.

I don't know about MN but I believe it most, if not all, states do not use support as a basis for terminating parental rights.

In most cases, it's not as simple as someone not wanting to contribute financially.

I don't know about MN either but in AZ child support and visitation are viewed as two different issues. A custodial parent can be in trouble with the court if visitation is denied even if child support has NEVER been paid. In my opinion, I think it's totally wrong to let someone have visitation rights if they don't want to help with everyday support of the kids but the court says it's ok... go figure!!