I very rarely have any issues, even in some of the most remote provinces, using a UK-issued Visa branded debit card in China. Very occasionally I encounter issues with (i) ATMs that are not attached to banks (for example in airports, shopping malls); and (ii) ATMs from some of the non-national banks (e.g. Pudong Development Bank). These seem to be down to communication issues betwen the ATM and the bank - the connection seems to time out and the transaction is then either accepted or rejected, depending on how the ATM has been programmed.

As others note, there can be transaction limits on machines. I have found ATMs that are limited to RMB800 or RMB1000 per transaction, even with domestic cards, and will decline requests for over that amount. Even the most generous machines will impose an RMB2500-3000 limit per transaction. For these machines, you can simply reinsert the card and repeat the transaction until you get the amount you want, though of course your transaction fees will mount up.