Apparently, with the Li-Ion batteries in our phones and electronics, fully discharging is bad for the device as it counts as one charging cycle when you bring it back up to 100. My Moto Defy, HTC Desire, and GS5 (though that one actually had its NAND tank after many years so that's a different problend) were fine as I used them all the time without relegating them to a secondary device, but my 6S, 6S Plus and Nexus 5 all had these sudden percentage drop problems. The 6S Plus would discharge exponentially faster between 0-30% and the 6S and Nexus straight up would just instantly lose that charge.
I don't know how your habits usually are with charging devices but I think you're doing the right thing here with a new genuine battery and maybe keeping it at as high charge as you can.