Don't know about MLB12 specifically (I doubt it's different from any other Vita game in terms of battery use), but I linked to this article a while back when the question came up:
http://www.computerandvideogames.com...-3ds-who-wins/
3 hours 47 minutes on full brightness. So....longer than that if you use a lower brightness setting.
More detailed IGN article:
http://www.ign.com/articles/2011/12/...-battery-tests