Only once?
Safe height to go around? Well I once hit the ground so hard that I decided to go around from the bounce. Guess that's pretty low.
Some of my bounces when I was learning to fly the cub I could just set up a new approach
Seriously, though, unless it's a one way strip or you are flying a glider, there are precious few times when it is impossible. I have converted a few glider pilots to powered aircraft and it is actually quite hard to persuade them not to try salvage a bad approach but to take another try at it. It's mindset and primacy again, what you learn to do first tends to stay with you