The rights to the series are owned by Alcon. They apparently had some difficulty selling the show originally, since it’s original distribution deal was a bit of a patchwork: the primary customer was SyFy who was trying to rebuild their portfolio, and purchases first airing rights, but didn’t have the commitment for streaming. Amazon picked up US streaming rights relatively cheaply, Sky picked up UK rights, and Netflix picked up most of the other streaming rights. SyFY by far had the highest financial cost.
It was never a cheap show to produce, and the nature of negotiating actors’ contracts makes them substantially more expensive as a show does well (since they start to get offers from other studios to work on their projects). After Season 3, it was too expensive for them for what they were getting (linear rights, not streaming), and their parent NBC was still building (and still is) their streaming portfolio. It was just too much money, and they dropped it. Alcon (and many fans) aggressively marketed to Netflix and Amazon, with Amazon picking up future streaming rights at a substantially higher price than they were paying, but it was now a really strong property (it’s been a substantial draw for Prime streaming).
Not to spoiler things too much, but they’ve hit two issues at once story-wise: most of the unaired book series material takes place after a substantial time jump, which is a bit of a casting challenge (recast? Age the actors? Rewrite material?), and they’ve got the increasing costs of the actors’ contracts as well. While no GOT for numbers, it’s a solid draw for Amazon with absolutely rock-solid reviews and ratings, so I guarantee Alcon is trying to work something out, but wasn’t able to break the barrier yet for future seasons and movies.
I expect that we’ll eventually see something worked out, probably a combination of movies (from unaired novella adaptations) and series, but it may be a while.
