Superconductivity is essentially an emergent phenomenon of many body electron system. I am wondering how much size reduction can it stand. Certainly no superconductivity exists for a single atom or perhaps for even a small cluster of atoms. So superconductivty cannot persist indefinitely and has to disappear for some small size.
Superconductivity is specific to the thermodynamic limit, however under the right conditions one can have superconducting correlations in even small systems. If we consider the off-diagonal long-range order, the practical limit is a size whereby such long-range order can be unequivocally identified. Similarly as regards superfluidity.
Here another manuscript that discusses a bit what phenomena become relevant for small superconducting particles: Mesoscopic superconductivity in ultrasmall metallic grains, http://arxiv.org/abs/1407.8547
I would actually recommend the articles from Kalus Kern's group provided by Joachim above. I recall having heard Klaus speak on the topic some years ago and that was actually a good and quite convincing talk.
A link has been made above to the case of superfluidity. beatiful experiments exist on the rotational spectra of molecules solvated in small He droplets (T~0.37K). If I remember right one might want to atribute the term "superfluid" to objects as small as having less than 100 atoms!
We studied magnetization of Lead NP in attached article.
Article Magnetization of Small Lead Particles
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