Says it all in the title, at what point did Norse Paganism cease to exist in Scandinavia? What contributed to its death? And just how long did it take to die out? Were there Pagans who lived in Christian Scandinavia? Did the Scandinavian Christians recognize the old gods, or old ways at all?
This doesn't really answer your question head on, but it's relevant to your question anyway.
Fakse-Brokke was a figure of wood, shaped like the head and torse of a man, that was worshipped in Setesdalen in Norway until the late 17th century. He's regarded as possibly being the last remnant of pagan worshipping in Norway. Setesdalen is a valley in the south of Norway, due to being relatively geographically isolated it was, and is, known for preserving much of the older culture of Norway longer than any other place, especially the most northern and most isolated farms and communities there. Oral traditions and old customs were kept alive for longer than in the rest of Norway.
A lot of writers have collected the stories and information regarding this, I've used what is written in Det Store Tidskiftet, Svein Hovet, 1969 - Folkeliv i Setesdal, pages 20-26 for the following information:
Fakse-Brokke was a god, or house god, possibly from the time of the change from paganism to christianity. He was placed at Hylestad (a farm), and was made out of trunk of a large pine tree. He had the shape of a human being, and was well tarred, with a hat of stone. He didn't travel anywhere, but sat inside the farm, and the people prayed to him for good tidings and favourable weather for their farming, to cure and prevent illness, and to help with romantic endevours. for a successful harvest, to cure and prevent illness, for help with romantic endevours, and all the other things people general use religion for. If Fakse was a god for the whole community, or if each household/farm had their own deity is hard to say anymore, but most probable each household had their own deity to worship. Farms were a long way apart, and it was a lot easier to simply go to your own god to pray inside a house than to travel. People offered him food, milk, and horseblood.
As time progressed, fewer people cared about him, praying to and believing in a piece of wood seemed silly to new generations, so the tarring and maintenance of Fakse-Brokke was not kept up, and when the last old people who still worshipped him passed away Fakse Brokke was put outside and used as a block for chopping wood. A while after that he was used as firewood. The person who finally chopped him into firewood was Torolv Faremo, born in 1798.
So one way to answer your question would be to say that paganism truly died when Torolv Faremo took the axe and unceremoniously reduced the once venerable Fakse Brokke to firewood (which happened sometime between 1820 and 1840).
Now, the historical accuracy of Fakse-Brokke is not debated. There are many sources describing it. People really did worship a wooden, tarred figure of a man wearing a stone for a hat until a couple of centuries ago at Hylestad. What is argued over is wheter or not this actually represented a genuine pagan worship of a deity. There are those that have argued that it does, but the opinion seems to have swung in favour of a more recent origin for Fakse-Brokke.
The Norwegian professor Reidar Th. Christiansen was of the opinion that Fakse Brokke was a catholic saint. Professor Olav Bø went even further, and argued that that the possibly carved figure might have been a sculpture saved from destruction during the reformation. He was then kept and worshipped until the information regarding his origin had blurred completely with folk beliefs. Possibly Fake Brokke came from the stave churches at Nomeland or Bjørgum. During the reformation, when the destruction of catholic art was widespread in Norway, some faithful believers chose to whisk away a sculpture of a saint or figure of worship for safekeeping at their farm, where they still worshipped him hundreds of years later.
The line between pagan religion and folklore is somewhat blurred in Scandinavia. A lot of the Norse pagan perfial figures, such as dwarves and elves (both of which were not very much like Tolkien's versions), trolls and giants merged into or morphed into the folklore of the early modern age - some of which survived into only a scant few years ago.
At times the church would actively work against these superstitions, somethimes it would try to link them with the devil or demons. Regardless, it was not capable of eradicating belief in them.
In northern Sweden, large boulders left in the landscape by hte retreating ice during the ice age was explained as the work of giants - they could not stand the ringing of church bells during Sunday morning and threw rocks in the general direction of the churches. Since they could not stand the sun either, they could not see where they were throwing these huge rocks, they missed and the rocks remained in the landscape, while the giants left as christianity spread.
The dwarves of Norse mythology, strong magical beings that created Thor's hammer Mjölnir (that always returned to Thor's hand after he threw it) and Oden's spear Gugner (which always hit) was made by the dwarves. It seems like these morphed into the house elf of Scandinavian mythology. These creatues, about 20-60cm in height and wearing a pointy cap were capable of powerful magic and were the protectors of the forests and mountains against trolls and giants. They either lived in underground lairs marked by three rocks of equal size lying in a row, or if a farmer was lucky, one of them could take up residence at a farm.
The house elf, if respected and treated well, would use his magical powers to care for the animals, increase the amount of grain in storage, repair and mend tools and buildings and generally be of a great benefit to the farmer and his family. Make no mistake though - he cared for the farm primarily - if he found the farmer to be a drunkard, a gambler or otherwise incapable, he could make bets or trick him into death or suicide so that a more capable man could take over the farm.
Families would place a bowl of fine porridge with a patch of butter for the house elf during christimas as a thankyou offering every year - if this was neglected, the house elf could go on a rampage, infect or kill the livestock, make the children sick or drown, make the harvest fail and many other things.
An anecdote related to this - in the early 1980s, my maternal grandmother desperately tried to convince her husband, my maternal grandfather to not blow a few rocks away where he was going to built a house - because the rocks were three rocks in a row of equal size and there could be an elf lair under them. My maternal grandfather would have none of it though, despite her pleas.
So, you could say that parts of the Norse religion survived as Scandinavian folklore and were actually acted upon well up to the 1980s.