This article is a good review of recent special elections to fill U.S. House and Senate vacancies.  One thing Chad should have mentioned is that a Senate seat can be filled by appointment, but the Constitution requires that a House vacancy can be filled only by an election.

When Mark Takai returned home and announced he would not seek re-election, that's when it would have been logical for him to resign to open the way for a special election.  I believe he never cast any vote or attended House meetings after then, so the seat was vacant in fact if not officially.  Why did he not resign?  Probably because Dem party bosses told Takai not to, for fear a Republican might be elected when Dems split their vote (as happened when Djou won because Case and Hanabusa split the Dems vote).  Dem bosses decided an empty seat with no voice for the people was preferable to letting the people elect a Republican.  Thus citizens in CD1 have had no rep for most of this year.