This would certainly depend on a variety of factors, as the other answers have mentioned, including plate tectonics, latitude of this particular fjord, and importantly the rock that makes up the fjord walls.
If we make the assumption that plate tectonics have not destroyed the area, and that the area is located in a fairly dry, cold part of the world, and that the underlying rock is resistant to erosion, a fjord could certainly still exist in some form after 250 million years.
According to this abstract from a University of Vermont study, granite will erode at rates ranging from 1 Meter/Million Years up to about 20 Meters/Million Years, so quite slowly.
The fjords on Baffin Island, for example, have huge granite cliffs (almost a mile high in some cases), and the island is quite cold and dry, and so an assumption could be made that their erosion rates will be towards the lower end of that range. So in the best case scenario, these fjord walls would have eroded 250 Meters in 250 million years, and so they certainly would retain a lot of the characteristics that make them fjords.