This is completely wrong. Modern cryptographically secure PRNGs can generate practically unpredictable sequences of as many numbers you'd like from an initial seed of >= 256 bits of entropy. This is actually how modern cryptography works in general: you wouldn't expect a 256-bit AES key to suddenly become insecure and predictable after encrypting a certain amount of data, would you? Why would a CSPRNG be any different?
In fact, both /dev/random and /dev/urandom are CSPRNGs. /dev/random is *not* a true RNG. It's just a CSPRNG that tries to reseed constantly and blocks when it can't based on an /estimate/ of the available entropy, but this constant reseeding is unnecessary for the same reason that we don't have to cycle AES keys constantly. It may make things harder for some contrived threat model when the attacker is able to glean your PRNG state periodically, but the practicality of this model is doubtful. djb has a very good article on this.