It all will boil down to how you define culture and it's survival. Last year (IIRC) a descendant of the Rambo family participated in a realityshow on Swedish tv featuring Swedish-Americans discovering their family history in Sweden. He clearly seemed aware and proud of his Swedish roots. What I'm saying is that it does to some extent depend on how people themselves see upon their culture and so rightly it is a question perhaps better answered by local historians.

I'm sourcing this basically from Herman Lindquist's 2015 book, "Våra kolonier - de vi hade och de som aldrig blev av", roughly "Our colonies, the ones we had and the ones that never were". He writes a couple of chapters about the New Sweden colony.

The Swedish presence was never that large, amongst the colonists and officials there was a fair number of foreigners. E.g. at one point a larger group of 80 Dutch settlers arrived to escape Dutch persecution and were allowed to join the colony. The colonial adventure was mainly the brainchild of the Swedish royal chancellor Axel Oxenstierna and after his death the project wasn't as interesting to the Swedish state. Swedish interests remained relatively fixed on more important matters at hand. It was also attempted during the apocalyptic wars of the 1600s and there was never really enough resources to spend on it either. The difficulty of the Atlantic crossing can also be seen in the number of ships that arrived in North America badly damaged by storms. In fact the man who had helped start the colony, Peter Minuit (yes that guy) died while in Swedish service during a visit to friends in the Carribean as the ships were struck by a bad storm. The European wars and shifting alliances also led to troubles, and it was during one such period the Dutch decided to get rid of the Swedes.

Now the Dutch conquest of New Sweden only lasted 9 years, when the Dutch were themselves replaced by British rule.

There was about 600 inhabitants in former New Sweden and 2/3 were Swedes and Finns, the rest Dutch, German and British. They were able to preserve local rule for a while with both Swedish courts and Swedish Lutheran churches. In 1669 there was small revolt against heavy British taxation but it was beaten down.

In 1693 the former inhabitants of New Sweden sent a missive to Sweden where they declared to be Lutherans of pure Swedish faith and following Swedish customs and asked to be sent Lutheran priests, Swedish bibles and other spiritual and educational material. The petition was signed by 139 families with 939 members, 39 who had been born in Sweden. The Swedish king Charles XI, deeply religious himself, sent them 3 priests and liturgical books that were available.

In 1749 Pehr Kalm, a disciple to Carl Linnaeus, arrived in Philadelphia (a city built on Swedish settlers' lands) to examine the North American nature. He travelled around the countryside and noted that the settlers still kept to many old Swedish customs and the older people could still speak Swedish though younger people were integrating with the local North-american British culture. Kalm notes his thoughts that the Swedish descendents are taking too much after the English. So I think we could in lieu of a better firm date (as it would be a process) say that around this time is when when Swedish culture fizzles out. With the caveat that it isn't necessarily for us to tell other people when their culture seizes to be.