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The classic example of "not enough randomness" is the Debian openssl vulnerability: https://www.debian.org/security/2008/dsa-1571 . But it isn't what you are imagining -- they didn't run out of entropy -- they just broke their RNG by removing all entropy sources.

There are no known issues with running out of randomness over time. The main reason to re-seed a CSPRNG is as a defense-in-depth against implementation flaws leaking state.

Probably all rng-related vulnerabilities in modern crypto are caused by unnecessary complexity added in order to prevent "running out of entropy" and not by not having enough entropy in the first place.

I remember some broken SSL certs generated during boot of some routers.