  Protection of gauge invariance in experimental realizations of lattice gauge
theories based on energy-penalty schemes has recently stimulated impressive
efforts both theoretically and in setups of quantum synthetic matter. A major
challenge is the reliability of such schemes in non-Abelian gauge theories
where local conservation laws do not commute. Here, we show through exact
diagonalization that non-Abelian gauge invariance can be reliably controlled
using gauge-protection terms that energetically stabilize the target gauge
sector in Hilbert space, suppressing gauge violations due to unitary
gauge-breaking errors. We present analytic arguments that predict a
volume-independent protection strength $V$, which when sufficiently large leads
to the emergence of an \textit{adjusted} gauge theory with the same local gauge
symmetry up to least a timescale $\propto\sqrt{V/V_0^3}$. Thereafter, a
\textit{renormalized} gauge theory dominates up to a timescale
$\propto\exp(V/V_0)/V_0$ with $V_0$ a volume-independent energy factor, similar
to the case of faulty Abelian gauge theories. Moreover, we show for certain
experimentally relevant errors that single-body protection terms robustly
suppress gauge violations up to all accessible evolution times in exact
diagonalization, and demonstrate that the adjusted gauge theory emerges in this
case as well. These single-body protection terms can be readily implemented
with fewer engineering requirements than the ideal gauge theory itself in
current ultracold-atom setups and NISQ devices.
