I accidentally left a holiday unpaid for approx one week before. I was called a couple of times on my mobile from a number that looks like one of the frequent cold calls everyone gets in the UK, so I left it unanswered. When I finally picked up it was some nice man at BA asking if I wanted to pay now. Don't know what would have happened if I'd have said no...
Of course, I'm not advising you to miss your payment because it will be fine, but noting that BA did not cancel my particular holiday straight away