The problem with many of these "deadbeads" is that they have a number of things stacked against them.
A sampling of statistics:
Not all "deadbeats" intentionally skip out on paying for their childcare. Actually, mothers who are non-custodial parents are less likely to pay for childcare than non-custodial fathers, but this is mainly due to their far lower income post-divorce.
Generally, I would say a valid excuse would be the inability to pay based on current employment and a reasonable standard of living. This goes for both mothers and fathers.