I assume it is the left sear that releases when you fire the right. If you were to fire the barrels in the reverse order next time you use it (before you take it to the 'smith) you might be able to determine if the second sear (presumably the left) might need the attention--rather than working them both over. The tips, if they are stoned to change the angle, should be rehardened when you get them right. The problem could be something other than the sear tip; it could be the stock has swelled for some reason and is impinging on the sears so they aren't engaging fully. That would require blacking it down, not a big job but takes some time. Hope this helps.
