The problem with child maintenance is that it is a blunt instrument, the service is overstretched, the law is laced with unfairness and there are not the resources to look at each case in enough detail.
The injustice we see most commonly on Mumsnet is where the ex-partner is self employed and then uses various means to reduce paying (e.g. working for cash, using a limited company and taking a small salary etc).
There are other problems with the system however which can create unfairness and can partially explain reluctance to pay. One of the big problems with CMS is that it doesn't properly take into account the shifts in the costs of housing in recent years, or the likelihood that the primary earner might also be the primary or equal carer.
Unlike court ordered maintenance, the CMS takes no account of what each respective parent is earning. When the lower earner has the children less than 50% of the time (and this is happening more and more frequently) they can find themselves getting trapped in a situation where they cannot afford to pay both rent on a property big enough to have their children and CMS.
For example, imagine mum is a well paid executive earning £150k and she decides to drop to £75k and work 2.5 days a week after divorce and dad's on £25k and can't afford to do the same thing and has to keep working full time. Mum gets the kids 60% of the time, takes home about £4k a month from her earnings and receives CMS from dad too (admittedly a lot of people wouldn't ask for this in this situation but it happens). Dad isn't even left with enough to put a roof over his head, so he begins working cash in hand because the alternative is a shared house that is unsuitable for his children.
I think CMS would work a lot more smoothly if it was based on the incomes (gross, not after pensions, and if one parent is an owner of a company it should be the whole profit of that company) of both parents and not just the payer. It would allow both for some recipients to get a more appropriate amount (CMS is often too low) but would also prevent the situation where a lower earning parent is unable to house themselves because they have to pay it to a wealthier spouse.