The Magnus expansion is attractive for periodically driven quantum systems because every finite truncation exponentiates an anti-Hermitian generator and therefore preserves unitarity. Its practical failure in interacting fermionic systems is nevertheless subtle: a low-order approximation may remain unitary while becoming progressively less accurate as additional terms are retained. We establish order-resolved breakdown signatures for a half-filled, periodically driven one-dimensional Fermi-Hubbard chain. The one-period propagator is computed numerically exactly in the fixed-particle sector and compared with Magnus approximants through fourth order. Failure is defined operationally by a successive-order error ratio (rₙ=εₙ/εₙ₋₁≥ 1), not by an unsupported claim of divergence of the infinite series. Across a raw (9×29) interaction-frequency grid ((U/J=0…,8), (ω/J=2…,16)), at least one added order loses improvement at 36.40% of the 261 sampled points. The smallest sampled frequency above which all retained orders improve throughout the remaining high-frequency tail rises from (ω/J=2.5) at (U=0) to (11.5) at (U/J=8). At (U/J=4), the highest (r₄=1) crossing occurs at (ω/J=7.719), followed by a monotone sampled tail from (ω/J=8). High-frequency error exponents approach the expected omitted-order scaling. A norm-based convergence certificate is consistently more conservative than the observed finite-order boundary. These results show that Magnus breakdown in the Hubbard model is order dependent, interaction shifted, and detectable before unitarity is lost.