Why do TV shows sometimes change the intro mid-season?

TV-shows sometimes have mid-season breaks (I don't know why, but that seems to be what they do). White Collar seasons 2 and 3 did just that, as you can see on the Wikipedia Episode list.

I would say that is the most likely cause, and should mean the Intro changed from Episodes 9 to 10 in Season 2, and 10 to 11 in Season 3.

Further to other answers, another reason the intro could change is due to holdover episodes. This is when some episodes in one production run are kept back and broadcast during the next season.

This happened with season 20 of The Simpsons - that season marked a shift to HD and widescreen, and with that came a new intro. However there were 9 episodes held over from the previous season, so the intro changed halfway through the season.

Layna answered your question well but sometimes the mid-season credits got changed even when there is no mid-season break. The intro gets changed to include new or remove existing cast and crew, or to add new or remove existing footage.

Take the case of Power Rangers or any anime show. They change Intro so many times mid-season from a minor change to a complete change. They remove the dead characters scene from the intro and add the new ones. I have seen same thing happening to TV shows too.

For examples refer to TV tropes article for Evolving Credits.

Or refer similar question about Game of Thrones:

Does the Game of Thrones intro change to reflect the current story?