For countable discrete groups \(\Gamma \), we consider \(\epsilon\)-representations of \(\Gamma\) into unitary groups \( U(n) \). These are unital maps \(\rho: \Gamma \to U(n) \) such that \( \|\rho(st) - \rho(s)\rho(t)\| < \epsilon \) for all \( s, t \in \Gamma \). Kazhdan has shown that the surface groups of genus \( > 1 \) admit \(\epsilon\)-representations which are far from genuine representations in the point-norm topology. We exhibit new classes of hyperbolic groups \(\Gamma \) which have the same instability features. More precisely, there exist a finite subset \(F \subset \Gamma \) and \( C > 0 \) with the following property. For any \(\epsilon > 0 \) there is an \(\epsilon\)-representation \( \rho: \Gamma \to U(n) \) such that for any representation \( \pi: \Gamma \to U(n) \), \( \max_{s \in F} \|\rho(s) - \pi(s)\| > C \).