Unlike arbitrage, the relationship is statistical rather than mechanical, so there is residual risk.
The failure mode is that the relationship changes rather than reverting - and the position was sized as though it could not. Several well-known blow-ups follow exactly this pattern: a convergence trade treated as risk-free, leveraged accordingly, held through a divergence that never converged in time.
Statistical arbitrage is the diversified version: many small, weakly predictive relative-value bets whose idiosyncratic risks cancel, leaving the aggregate edge.