100 is not typically considered an adequate number of iterations for estimating error rates (or for estimating proportions more generally). And the fact that a particular run of 100 iterations happened to produce a similar result as a particular run of 1000 iterations does not justify using such a small number. In fact, performing several runs of 100 iterations each, without changing any parameters, will produce error-rate estimates that are quite variable from one run to the next.

Consider a case where 100 iterations produce an estimated proportion of .05. The 95% confidence interval for that estimation is extremely wide: [.020, .111] (using Blaker's exact method, as implemented by the blakerci function in R with the PropCIs package). Consequently, one cannot say with confidence whether the true proportion is far below, far above, somewhat below, somewhat above, or very near the .05 estimate. Thus, error-rate estimations that are based on only 100 iterations are typically not very meaningful.

To illustrate this problem, below is a simple R program that uses simulations to estimate the Type I error rate of a one-sample t-test with an alpha level of .05. Obviously, the actual Type I error rate should be .05. Run the program 20 times or so with numSim set to 100 (meaning 100 iterations), and you will likely get several accurate estimates of .05, but also several inaccurate estimates that are much lower or higher than .05 (perhaps .03, .08, etc.). On the other hand, if you set numSim to 10^6 (meaning a million iterations), you are likely to consistently get estimates that are very near .050 (though it will of course take considerably more processing time).

numSim = 100 # number of iterations
n      = 10  # sample size (number of observations per iteration)

# matrix of random values from std normal distribution (rows=subjects, columns=iterations)
y = matrix( rnorm(numSim * n), nrow=n )

getP = function(x) t.test(x)$p.value # function to get 1-sample t-test p-value from a vector
p    = apply(y, 2, getP) # apply that function to each column of y to make vector of p-values

mean(p < .05) # output estimated Type I error rate