According to Robert Sneddon on Quora, there were conflicts between distributor/production companies (Walt Disney and Walden Media, respectively) and Lewis Estate (owner of Narnia copyright). The Chronicles of Narnia 1 was a huge success and they decided to make sequel. However, it somehow underperformed and they were not happy with the profit the sequel made. Meanwhile, Lewis Estate were unhappy either with some aspects of the second film`s screenplay.
Article suggests that, after Walden Media lost filming rights of Narnia in 2011, The C.S. Lewis Company offered the rights to Mark Gordon Company to adapt the 4th sequel - The Silver Chair. Since then, there wasn't much updates about the movie. Until 2016, Sony joined the party to finance the production. The new idea was to reboot the franchise with different cast due to the original casts of previous Narnia movies had aged out.
It didn't work out, no one knows what exactly was the cause of production fallen off the track. It is speculated that Sony later decided to brush off the old and long-forgotten franchise, not to mention the gross profit after the 1st movie did not meet Walt Disney's expectation.
You may refer to Wikipedia as mentioned by Rahul. In November 2018, Netflix acquired the rights of all seven Narnia novels to work on TV adaptation. It seems the reboot is very likely to happen, but its future is still uncertain. Just few months ago, in May 2020, it was reported that movie producer of Narnia - Douglas Gresham (also Lewis' stepson) has admitted he hasn't heard any updates about Narnia's production from Netflix in a while.
IMO, Narnia franchise will come back, given The C.S. Lewis Company and Netflix had made multi-year agreement for the rights just two years ago. Perhaps Netflix needs more time for careful planning due to the potential and expansiveness of the series. It's been a long 15 years since The Chronicles of Narnia 1, and things changed. Let's not give up hope even there is so little news about it.