As I have noted in earlier posts, some of the medieval Greenland Norse assimilated with the natives of North America at least as early as the 12th century. I believe it will eventually be proven that this process began soon after the Norse settlements were founded on Greenland in 986 by Eirik Thorvaldsson.
It seems that assimilation with the native peoples also began occurring with their Viking brethren on the European continent by the 11th century. After a couple generations of conflict they stopped returning to the homeland.
They began to permanently settle with the the inhabitants of lands that they conquered and/or traded with from Ireland to Russia, adopting their languages and customs. Researchers at the universities of Leicester and Nottingham, in England, recently found that up to half the DNA from men in northwest England matches Scandinavian genetic types. Raiders or Traders? Andrew Curry, (Smithsonian Magazine, New York, NY, July 2008 - 29).
To check the proliferation of the Norse DNA Haplogroup throughout the medieval world, I recommend clicking on the link to an excellent WIKI article on the subject: R1a1
The Viking Age endured about 400-years. During these centuries the men gradually stopped returning to the homelands at the conclusion of each summer's season of raiding and trading. The distances became too great, the voyages too hazardous as the Mini-Ice Age settled over their areas of influence in the northern hemisphere.
The process of assimilation throughout the Viking World, from Constantinople and North Africa, across the North Atlantic Ocean to Greenland and L'Anse aux Meadows, Newfoundland finally ensured that the sun would set on the young men who had gone iviking.