A theory isn't completely abandoned just because of a single contradicting observation. The theory may explain a host of other phenomena very well, in which case then new observation merely shows a limit past which the theory no longer applies. As an example, we know of many observations which contradict the predictions of Newtonian gravity, but we still use that theory for planning space probe trajectories.

I would like to know what you mean when you say "big bang theory". I think that would help ensure we're all talking about the same thing.

When I say "big bang theory", I mean the idea that the universe we live in was in a very hot, dense state roughly 13.7 billion years ago, along with some other details such as a brief period of cosmic inflation.