No, it's not tied to the number of times you've used a particular item on the anvil. There's a random chance each time you drop an item, regardless of what happened to that item previously. I've had things cursed the first time I've dropped them, for instance.
The Dredmor wiki says that it's 2/7 chance of a curse, and a 5/7 chance of a blessing.
I'm always torn between using a really good item on it, in the hopes that it gets better, or using a kind of "meh" item in the hopes that it either becomes good or destroying it won't matter. Frequently what I'll do is try to use something that I have a duplicate of, or at least a backup for that slot. That way if it gets better, it's a win, and if it gets worse, oh well, I've got a backup.