= Solution
A <magnetic field> varying over a length $\ell$ has $|\nabla\times\mathbf B|$ of order $B/\ell$. Consequently, the resistive <magnetic energy> loss contains two inverse powers of $\ell$, while the <resistive magnetic-helicity balance> contains only one. Small-scale gradients can therefore dissipate substantial <magnetic energy> while retaining an approximately conserved large-scale <magnetic helicity>.
A dimensionally consistent version is the <selective decay bound for magnetic helicity>. With $D_B=\eta_m\int_V|\nabla\times\mathbf B|^2\,dV/\mu_0$, the <Cauchy-Schwarz inequality> gives
$$
|\dot H|\le2\eta_m\left(\int_VB^2\,dV\right)^{1/2}\left(\int_V|\nabla\times\mathbf B|^2\,dV\right)^{1/2}
=\boxed{2\mu_0\sqrt{2\eta_mE_BD_B}}.
$$
For bounded $E_B$ and bounded, possibly nonvanishing $D_B$ as $\eta_m\to0$, the resistive change in <magnetic helicity> tends to zero, even though resistive <magnetic energy> loss may remain finite. \b[Magnetic energy is preferentially dissipated, while magnetic helicity is approximately conserved in this bounded-energy, bounded-dissipation limit.]
This is not a comparison of quantities with different physical units or a universal ordering of fractional decay rates. For a single <Beltrami field> satisfying $\nabla\times\mathbf B=k\mathbf B$, both integrated quantities have fractional decay rate $2\eta_mk^2$ without fluid motion. The boundedness assumptions and distribution of <magnetic helicity> across spatial scales matter.
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