@jj13
When we enquired about renouncing, a couple of years ago, the PSB told us it would take some months, as the papers had to be processed in Beijing. They added that there was a small possibility that the renouncing might be rejected!! I doubt that would occur if one or more parents were foreigners, but...!

@jj123
We have zero intention of renouncing our dual nationality childrens' citizenship. US citizen's must pay about USD 150 a year for visas, so Chinese would reciprocally have to pay USD 150 a year for visas. Although the sum isn't exhorbitant, depending on what one considers exorbitant, why would I pay for something I don't need to pay for, that should be gratis?

That's my issue - I'm a cheapskate skinflint...when it comes to giving money to the government (regardless of sovereignty).

This doesn't add an awful lot to the previous discussion, but I received this from "UK Gvt Email Alerts" last week:

China doesn’t recognise dual nationality; any person born in China to a Chinese national parent will be considered by the authorities to have Chinese nationality; if you have both British and Chinese nationality you may be treated as a Chinese citizen by local authorities, even if you enter China on your British passport; if this is the case, the British Embassy may not be able to offer you consular assistance; if you’ve formally renounced Chinese citizenship, you should carry evidence that you have done so.