I found statement in an article "Good Practice in ( Pseudo ) Random Number Generation for Bioinformatics Applications" that you should not use too many random variables in a single simulation. Authors says that it maximum number of random values taken from PRNG should be $\frac{p}{1000}$ or even better $\frac{1}{200}\sqrt{p}$. $p$ is the period.
But I cannot see any references in other articles.
Do you know any reasons why not to use more values ?
Assuming $p$ is the period of the PRNG, this is good advice, because after $p$ values are taken the PRNG will repeat.
To avoid the issue, just use a PRNG with a very large period. It will barely take $O(\log p)$ time to extract each pseudorandom bit, so you can make $p$ much larger than the number of values you will ever need to extract.