The ability to have the pads centered (or really both sides releasing from the rim enough to not rub) is dependent on the caliper spring to be in a position such that both sides of the spring move outward somewhat equally. This spring's rotational position is determined by the center bolt's rotation. The spring goes through the "block" which is secured to the center bolt, where the bolt goes so does the block and then the center portion of the spring. So by rotating the center bolt (and many better brakes will have a wrench fitting to make this easy) so that the spring (arms/pads) are roughly centered then keeping the center bolt in this position tighten it's back nut to trap it where you rotated it.

This is the first step to centering classic single pivot side pull calipers. The second step is to fine tune centering by bending the spring a small bit. Either by placing a punch against the spring JUST as the spring exits the center bolt's "block" and tapping the punch with a hammer. Or by detaching the spring's end from the arm's tab and pulling that side of the spring out and up to increase it's strength. These two methods are somewhat destructive in that you are purposely "damaging" the spring. If done with a crude and heavy hand the results will be worse then when you started. But with an experienced hand are quick and long lasting fine tuning tricks.

The cable routing and how much this effects the caliper's willingness to stay where you center it is another issue to be aware of. If the cable routing/loop shifts (as with rear cables that slide through top tube casing guides as the handle bars are turned) then this loop will pull and push on the cable side of the caliper. You can mimic this by just pulling on the casing and watch the pads move off center. So sometimes you need to trap the casing from moving. Better casing control will make the caliper adjustments longer lasting. Andy.