Initially you estimated:

$Y=\alpha+\beta_1X~~~~~H_0: \beta_1=0$

Then you accept or reject this at some confidence level (you were able to do that at 99%)

Now: 

$Y=\alpha+\beta_1X+\gamma Z ~~~~~H_0: \beta_1=0$

Now you fail to reject at the 99% level and you reject at the 95% level. 

If those extra Zs belong in the true model, then you ignore the first regression as it was biased. The regression that includes more relevant variables will result in less omitted variable bias and you can have more confidence in the results. 

Before you likely had a higher chance of type 1 errors because of omitted variable bias, while the newer specification is a better model.

To answer your added part: If you add extra data points and your results change, then you should maybe estimate the model for all the available data using the fuller model and then determine whether you reject or accept at 1% or 5%. 

So suppose you reran the full regression on the whole dataset and now you can only reject at the 5%. You would say that you reject the null that X is unrelated to Y, conditional on all the other variables, at the 95% level.