I'm in my university's team for the ACM ICPC [1]. We practice about one or two times per week, where each practice session is 5 hours. Some of the stronger programmers really practice this stuff every day. cf. Nick Wu's description of his preparation for programming contests [2].
[0] In 5 hours, the large input sets will be judged. I might move up or down the rank list depending on whether my answers for the large input were correct.
[2] http://www.quora.com/Specific-Quora-Users/Nick-Wu-Did-your-t...