So SRAM brakes have, in the past, had a little issue with the master cylinder pistons swelling over time, often when heated (such as when you leave your bike out in the sun). The only fix for this is to replace the pistons with the newer revisions that have more clearance between the piston and the master cylinder bore.
It turns out that this process is a bit tricky, as the piston is retained in the master cylinder by a snap ring, but it's too deep to reach with standard snap ring pliers, which I only discovered after buying the wrong ones. Luckily the right ones aren't too expensive, and the obstacle was soon surmounted.
I also decided to make a video of the adventure, which you can watch here.