The break-in procedure that I use on button rifled barrels takes about 100 rounds or so, and I have noted a steady improvement in accuracy as the break-in progresses that generally levels out after 100-200 rounds.
I have never kept a rifle long enough for accuracy to degrade, but I have owned a few that were already that way when I got them. Here's the transition from the throat area to the rifling from a Mark X Mauser in 7mm RM that looked really low-mileage on the outside, and a peek down the barrel with a bore light showed what looked like a shiny new barrel:
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I finally concluded that somebody must have played "The Rifleman" with this gun, shooting it quickly without letting it cool down between shots. - It's the only explanation I can think of for a new-looking rifle to have its throat cooked so bad.
I saw something very similar on a nice little .243 that I bought used, one time. The rifle looked pristine, a peek down the bore looked good - but when I got it home and bore-scoped it, I knew I'd been had. So far, I've never gotten good accuracy out of a gun that had the throat area fried like that.
Strangely enough, I have not seen nearly as much improvement in accuracy as the first 100-200 rounds are fired from barrels that look pretty smooth to start with, hammer forged barrels for example. They do however become less 'sticky' after a while, and copper does not adhere so readily. - Sometimes I think it may be due to a thin, persistent carbon build-up instead of polishing that causes this to happen. ( At least in part ) Like the carbon-based non-stick finish one gets on a seasoned cast-iron skillet.