The flapper fixed the problem for a short while, but ultimately the slow leak resurfaced. I went back to Duff's to readdress. The guy at the counter suggested that it may not be a flapper problem at all. Instead, he suggested that the problem might be a siphoning issue. Pretty cool, right? Well this time, he was spot on.
If you notice in the picture below, there is a black tube that extends from the flushmaster down into the white overflow pipe?
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This tube cannot be too long. If it extends too far down the overflow pipe (white pipe pictured), then siphoning can occur.
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I used a household scissors and clipped the tube and now finally the problem is officially corrected.