Netflix didn't drop the show, Syfy did--the situation was kind of a mess. Alcon produces the show, and then licensed it out to Syfy for first-run US cable viewing, and to Amazon for second-day US streaming. iTunes, the Microsoft store, and Google play also got the licensing both in the US and Canada Space got the live airing rights in Canada. Alcon then licensed the international streaming rights to Legendary, who sold it to Netflix (with a several month delay between when a season airs and when it goes up on Netflix).
Everybody involved--Syfy, Amazon, Netflix, Space, paid Alcon for the show, which allows Alcon to produce this super-expensive tv show. Problem is, Syfy could only make money on the show from the cable viewing and ad revenue, and most of the people watching the show didn't watch on live cable tv (considering the cable version of the show on Syfy is censored, has a lower-quality picture, and is constantly interrupted by commercials, who could blame them?). Syfy wasn't making enough money (not helped by Syfy not properly advertising the show), so they dropped it, leaving Alcon to scramble to find someone else to pick it up, and Amazon did (yay).
Netflix apparently wasn't interested in picking up the show after Syfy dropped it--according to the props master, Jim Murray, Netflix already had enough shows filling the niche The Expanse would have occupied. Obviously they weren't particularly interested in US streaming rights either when the show was starting out (also I bet Amazon just plain outbid them since Jeff Bezos is clearly a fan).