Are North Island Robins a species of concern? I notice in two of the three photos you uploaded to the gallery the robins have multiple bands, assuming they're for ID purposes?
With a little hyperbole, most birds in New Zealand are banded.
With the particular North Island Robins depicted here, though, they are either at Zealandia which is a fenced mainland sanctuary to which the original birds were introduced or on Tiritiri Matangi Island which was revegetated from farmland and hence the original birds there were also introduced. In both places most of the endemic and native birds are banded. (Just a quick side-track, the 1000th Stitchbird chick was banded at Zealandia recently).
However, many species of birds are routinely banded in "natural populations" also. You might have noticed that the Stewart Island Robin pictured is also banded, and Stewart Island is the third-largest of New Zealand's islands. For a number of New Zealand birds pretty much every individual is known (albeit not the case with robins, apart for the Black Robin on the Chatham Islands).