Why would it have to re-occur again and again? If the mutation is beneficial to the reproductive success of an organism, by definition their mutation will be passed on with no need for it to occur again by chance. The percentage of the population with the mutation would grow, potentially very quickly if it was a strong advantage over the previous generations. You're also characterising evolution as if to get from amoebas to humans you require a series of billions of independent coin-flips which isn't an accurate model, rather each generation is building on that which preceded it. Take the eye as an organ for example, it predates humanity by a very long time and was not independently evolved by humans - there was no need for it to have been since those genes already existed.
The predictions of evolution are generally supported by the available evidence at any rate, if you'd like to overturn it you'll have to propose a theory that explains the evidence more compellingly.