What lowers the p-value besides the sample size? The title pretty much says it. Sorry, it's so unspecific, I am not asking the question for myself and I am not familiar with stats.
 A: p value is a function of effect size and sample size. 
A larger effect size and a larger sample size will yield a lower p value (the question seems to imply the opposite). 
A: Maybe that is already subsumed in Peter Flom's definition of the effect size, but a higher signal (for me, that is the effect size) to noise ratio: for example, in a regression context, your t-statistic would be
$$t=\frac{\hat\beta_j-\beta_{j0}}{s.e.(\hat\beta_j)}$$
where $s.e.(\hat\beta_j)$ is the $j$th diagonal element of $s^2(X'X)^{-1}$. Here, $s^2$ is an estimator of $\sigma^2$, the error variance.
A larger $\sigma^2$ will, all else equal, tend to produce larger $s^2$ and thus translate into a smaller t-statistic and hence a larger $p$-value.
A: The p-value is defined as the probability of obtaining results at least as extreme as your actual data under the null hypothesis. The same data will yield higher or lower p-values depending on what exactly the null is, eg one or two sided, multi- vs univariate, etc. For example, in a multiple regression, an omnibus test may come out significant even though the slopes individually do not. 
