Re-using random values may compromise security.
(bad code)
Suppose an Encryption algorithm needs a random value for a key. Instead of using a DRNG (Deterministic Random Number Generator), the designer uses a linear-feedback shift register (LFSR) to generate the value.
While an LFSR may provide pseudo-random number generation service, the entropy (measure of randomness) of the resulting output may be less than that of an accepted DRNG (like that used in dev/urandom). Thus, using an LFSR weakens the strength of the cryptographic system, because it may be possible for an attacker to guess the LFSR output and subsequently the encryption key.