  The dynamics of lattice gauge theories is characterized by an abundance of
local symmetry constraints. Although errors that break gauge symmetry appear
naturally in NISQ-era quantum simulators, their influence on the gauge-theory
dynamics is insufficiently investigated. As we show, a small gauge breaking of
strength $\lambda$ induces a staircase of long-lived prethermal plateaus. The
number of prethermal plateaus increases with the number of matter fields $L$,
with the last plateau being reached at a timescale $\lambda^{-L/2}$, showing an
intimate relation of the concomitant slowing down of dynamics with the number
of local gauge constraints. Our results bode well for NISQ quantum devices, as
they indicate that the proliferation timescale of gauge-invariance violation is
counterintuitively delayed exponentially in system size.
