I'm not sure if you're insisting on examples in which a mathematician (or group of mathematicians) works single-mindedly on a single problem for many years and finally conquers the problem.  If so, then the following might not qualify.  But it might qualify if your conditions are not as stringent as that.  I quote from Ilse Fischer's <a href="http://www.ams.org/news?news_id=4726">response to being awarded the AMS Robbins Prize</a>.

> The idea of working on Robbins' last open conjecture on alternating sign matrices slowly manifested in my mind when I was writing a grant proposal about 10 years ago, when I identified it as an ultimate, albeit unrealistic, goal. In the beginning I hardly dared spend much time on it, but every now and then I discussed it with other combinatorialists. Roger Behrend and Matjaž Konvalinka were obviously among them, but I also had a particularly fruitful exchange with Arvind Ayyer back in 2012, which led us to several conjectures on the enumeration of extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order. About three years later, Arvind, Roger, and I were able to prove these conjectures, and to some extent also this work paved the way for the eventual proof of Robbins' conjecture. I feel deeply honored and moved to receive, together with Matjaž and Roger, the David P. Robbins Prize.