I've been reading some of the recent episodes of Gakuen Alice, and Mikan had her memories of the past two years (since she stared at the school) wiped. When she seems Natsume, however, she ends up remembering him. Are there any explanations about how it works or why it fails? I didn't see any, but I might have missed them.
Mikan seems to remember Natsume because of the alice stone . (Chapter About Creating Alice Stone) , When Natsume give the Alice stone to Mikan , it was nullify and each fragments came back to her . (sorry for my bad english) one of those fragments was About the One she loves . At first it was fuzzy to clear those memories that step by step occuring into her mind when Natsume give that alice stone everything becomes clear .
" Natsume pulls out the bag containing her tiny Alice stone, the first one she gave to Natsume when they were 12-years-old. Natsume hopes that by returning the Alice stone to Mikan, its proper owner, she will regain her memories, especially him. He gives it to her, and when she takes it, it is suddenly absorbed into the palm of her hand, which means that she has regained some of her Alice"(http://gakuenalice.wikia.com/wiki/Gakuen_Alice_Chapter_179)
In this manga they want to make people understand that love overcomes all. Especially love of the sort they have. Also, she had given him an Alice Stone in which magic (which also indicates memories of that person). If I'm not mistaken, she touches this stone when they meet and regains her memories. But why she would remember Natsume's name could also be explained with the amount of strong memories. Strong memories (love overcomes all) tend to be more often remembered. I think you've got your answer right there. :) This is not explained in the manga, it is only my own reflections.