Q. The date of the birth of Jesus is supposed to be 25th December, in a stable. How long did the family stay in that stable, that is, when did Jesus leave his manager crib and move to other accommodation?
First, Jesus was actually most likely born in the spring, not the winter. Joseph and Mary traveled from Nazareth to Bethlehem specifically to register for a Roman census. The Roman government would not have required its citizens to travel en masse back to their home towns in winter, when travel was difficult or impossible under the conditions of the time. The return of good weather in the spring is when the census would most likely have been held. However, the Christian church decided to celebrate the birth of Jesus on December 25 because of the symbolism of light coming into the world around the time of the winter solstice.
Second, since their trip to Bethlehem was for the census, Joseph and Mary would not have been planning to stay there very long. They probably would have wanted to visit with family for a while, since that was the town Joseph was originally from, but then they would have returned to their lives in Nazareth. Their trip back was likely delayed when Mary gave birth to Jesus, but even so, they would have traveled back to Nazareth as soon as mother and child could do that safely. So I would say they were in the stable (which was the only accommodation available to them, since so many others had also come to Bethlehem to register) probably not for more than a week. That would be my estimate, anyway.
The marvel is that the Son of God willingly was born into such a rough and improvised setting when he came to earth to be our Savior. Hallelujah!