Of the many interesting things to learn from H. L. Mencken's The American Language, some are to be found in its section, near the end, on foreigners living close together in America and how their language evolves. One famous such group is the Pennsylvania Dutch, who were not actually Dutch but German. They were called Dutch, not because of any confusion but, according to Mencken, because they called themselves Deutch (pronounced in their dialect as Deitch, though the diphthong is pronounced oi in standard German) which, of course, is German for German.
Mencken writes about how Norwegians, Germans and many other groups began to use English terms in their regular speech amongst themselves, providing very many fascinating examples to illustrate what appears to be a gradual trend towards an increasingly Anglicized language.
It occurs to me that I know of no similar examples today. Most immigrant English I have heard is rather high-functioning, but when I hear immigrants talk amongst themselves I never really recognize any words at all, although some book titles (like Econometrics) are obvious exceptions. Society is of course different in many ways today compared to the 1930's when Mencken last amended his great work of linguistics. If my casual observations are right, the question is in which ways society has changed to make immigrants use fewer loan words among themselves.
One possible way is telecommunication. When Mencken wrote, I believe there was no trans-Atlantic telephone line whereas today it is easy to get on Skype with almost anyone else in the world. Even before Skype, telephone communication has of course been feasible and inexpensive for several decades. It strikes me that any possible decline in English influence in immigrant lingo attributable to more contacts with the Mother Country should be discernible provided that immigrant speech has been continuously studied.
Another, more dire, reason, is that regulations have made immigrants harder to hire (think minimum wages and work safety, for instance), and that we are more regulated today than we were in the 1930's. If immigrants as a result associate less with the indigenous population, their language will not be as influenced. I reckon this explanation might fit some refugees or asylum seekers who come to escape in addition to finding work, but persons coming in specifically to seek work are not captured by this explanation, since they simply cease coming when opportunities decline.
Maybe there are other contenders to explain my casual observations. Or maybe my casual observations are wrong. Comments with information on these issues are greatly encouraged.