When molecules are driven by intense laser fields linearly polarized along the internuclear axis, their ionization rate vs the internuclear separation $R$ is known to have a maximum at some critical intermediate separation ${R}_{c}$. We show that such a maximum should occur only in molecules whose highest occupied molecular orbitals (HOMOs) are such that the electron cloud is concentrated along the internuclear axis (i.e., $\ensuremath{\sigma}$-type HOMOs). For molecular systems whose HOMO symmetry prevents electron probability distribution along this axis, we find that the ionization rate increases monotonically with increasing $R$ until saturation occurs. In other words, for such molecular systems, there is no critical ${R}_{c}$ at which molecular ionization is maximum.