How small of a time loop do we need before we can treat time as an instant in a Newtonian way?
In a purely scientific sense, it would have to be infinitesimal. As long as there's some definite, measurable size to the loop, then we can draw a tangent along that loop and treat time as linear in the immediate region surrounding the tangent.
In our own experience, if a time loop exists at all, it would have to be eons in size.