Let $\Phi:\mathscr B\to\mathscr A $ a functor between categories which preserves small limits (colimits).
There are non-trivial conditions on $\Phi $, $\mathscr A $ or $\mathscr B $ which makes true the implication $$\Phi\,\text {preserves small limits (colimits)}\implies\Phi\,\text {preserves all limits (colimits)?} $$
This question come from the fact that a small colimit (limit) can be seen as a universal (couniversal) arrow in suitable diagram categories, while this is not the case for large ones.