Are you talking about the issue with repeated k-values in ECDSA signatures?  In principle EdDSA (as used with Ed25519) has the same problem.  However, DJB's reference implementation uses deterministic k-values (as, I suspect, do all implementations of Ed25519) to avoid the need for a crytographically strong random number generator during signing (you still need a cryptographically strong random number generator for key generation, though!)

This solution isn't unique to EdDSA, though - deterministic k-values can and are used with conventional ECDSA, too.  RFC6979 defines one such  implemention, and I believe that some Bitcoin wallets actually use this.  The difference is that ECDSA (like DSA) is conventially defined and implemented with random k-values (like DSA) meaning that most implementations have an unnecessary vulnerability in the event of a poorly-seeded PRNG.