Lots and lots of loping circles! Seriously, that was 95% of the riding I did as an assistant at a reining ranch, lol. In addition to keeping them in amazing shape, you're focusing on keeping the shoulder up and the horse round and collected. You're getting them to consistently maintain the cued speed, with smooth & immediately adjustments to that speed whether asked in the center of a figure 8, random places on the circle, or before or after a lead change. Lots of counter cantering, both in circles or diagonally across the arena, so they aren't anticipating lead changes, too. Sliding stops are tough on the legs, so you only do what is necessary, and that depends entirely on the horse and how well the rider sets him up.
There are 10 approved NRHA patterns, but IME, people rarely practice the actual patterns because they don't want the horse anticipating. For instance, the patterns all have 4 spins each direction - you'll probably practice your spins in groups of 5-6 at home so your horse doesn't learn to fade or slow on his final 4th one, as that would decrease your score. You may opt to lope 3 circles one way and 4 the other, before going for a straight run and stop. You'll also rarely (if ever) ride a reiner along the fence/rail - he needs to go precisely where you're telling him, not because the fence line directs him; in the patterns, run downs have to be straight lines at least 20 feet from the fence, and you don't want your circles becoming oblong ovals at the top from a horse fading toward the fence.
Really though, all "maintaining" has to be tweaked to the individual horse, his level of training, and his rider's ability level - same as any other discipline.