  Unlike the bewildering situation in the $\gamma\gamma^*\to \pi$ form factor,
a widespread view is that perturbative QCD can decently account for the recent
\textsc{BaBar} measurement of $\gamma\gamma^*\to \eta_c$ transition form
factor. The next-to-next-to-leading order (NNLO) perturbative correction to the
$\gamma\gamma^*\to \eta_{c,b}$ form factor, is investigated in the NRQCD
factorization framework for the first time. As a byproduct, we obtain by far
the most precise order-$\alpha_s^2$ NRQCD matching coefficient for the
$\eta_{c,b}\to \gamma\gamma$ process. After including the substantial negative
order-$\alpha_s^2$ correction, the good agreement between NRQCD prediction and
the measured $\gamma\gamma^*\to \eta_c$ form factor is completely ruined over a
wide range of momentum transfer squared. This eminent discrepancy casts some
doubts on the applicability of NRQCD approach to hard exclusive reactions
involving charmonium.
