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It seems to me that the better question is what causes a page to stop being gray-barred. The only thing I've ever spotted that works is a good link from an external (unrelated?) site, and I'm not at all sure about that.
But why does it have to take many days, weeks or months since acquiring the backlink? - It appears to me that a delay in updating the reports in WMT will also result in a delay in improvements seen in the SERP's.
Does Google update this section in WMT more frequently for some sites than others?
Ranking is iteratively calculted several times a DAY, updated in real time.
Its like saying that we in the UK have only just gone into recession. It was only officially announced this week (after statistics show 2 Qs negative growth), but the EFFECTS of the recession have been felt for months. Just because WMT is only showing the data now doesn't mean the SERPs have not taken it into account for a while.
BTW, the strength of a link matures over time. Full value might take between 6 to 24 months to show.