Both London and Edinburgh had the physical power to end the border reaving any time in the sixteenth century; they just needed to send out magistrates who would consistently enforce the law and hang cattle thieves. It wasn't that they couldn't catch the reavers; there are lots of court cases against various raiders. It's just that they tended not to actually hang them except in the most egregious cases.

They didn't because both sides found the reavers useful in wartime as light cavalry scouts, and in peacetime as a means of putting pressure on the other. Since James VI-and-I was king in both capitals, he had no need for a bunch of dubiously loyal border bandits, and hanged them accordingly.