One possibility is that the first life just spread so fast that it ate all possible competitors. You aren't going to see life originate again now because life is already everywhere, and will just consume any batch of chemistry that starts getting life-like enough to be nutritious.I think a better question might be why has abiogenesis happened only once on Earth. Instead of several times or even happen today.
Another more outside possibility is that Earth life actually originated on Mars and was carried here by meteorite. In that case life from Earth never had a chance to originate. As for finding evidence of that; if life is discovered surviving underground on Mars and turns out to be multiple-origin, one of which appears to match Earth-life and the rest don't that would be good evidence.