I had the same situation with trying to thin out that "customers with a balance" list, and there seem to be safeguards in place to keep a person from deleting things on a whim. But there are a few ways to approach this.
For instance, if it doesn't work by using the "Find Sale" function (which it often doesn't), sometimes it will work if you go into Customer info and the Advanced Payment window, and look up their history. I don't remember exactly how, but you can get the invoice deleted there. Sometimes.
My last resort is going into the Manager window, then the Sales window. Be careful in there, I deleted ALL my sales once!!! (good thing for backup!) Anyway, that always seems to work, though it's a little more difficult to navigate.
Understand that I did this on my own and not on Ronald's advice - so it may not be recommended. But it seemed to work.