I would wager permutation tests inflate the false negative rate in a small sample. Here's an extreme example to illustrate, but this applies with less extreme examples too:
- r=1 with sample size 4
- there are 4! = 24 permutations
Therefore: at least 1/24 ( = .042) permutations will have r=1 so p(r=1) >= 0.42. This is far greater than the real p-value of r=1, which is practically 0. The worst part is, with a p-threshold of .01, this result is not significant. Which is crazy; r=1 is the most significant possible.
This is because when you shuffle among existing values, you are not getting a true null distribution. The existing values are shuffled in order but not value. The values themselves are quantized. The values contributed to significance. This can, and will, bias the "null" shuffled distribution to something more significant. This holds for r-values less extreme than 1, and should be true for models other than correlation.