Last Order (I suppose that's her official name?) seemed to imply she went after Accelerator on purpose. In some odd way, the core of the MISAKA network actually seems quite fond of the person who murdered her 10,000 times.

At first I was speculating that this was due to her not being....ripened properly, but then she gave that long discussion in the diner about how he must not be a bad person because he kept trying to scare her off and whatnot. Maybe despite the alternate opinions of certain individual MISAKAs (notably 10031 and 10032's affection for Touma), Last Order having spent all the other time "playing with" Accelerator, prefers him.