I had one female friend as a child, and she did exactly that. She moved to my city and joined my school in grade four. She wasn't outcast for being new or anything - kids in my school were all diplomatic or military, so there were new ones coming and going all the time - but for some reason, she chose to befriend me for no apparent reason, even inviting me for games and sleepovers. It lasted not quite a year before she abandoned the "friendship." She had plenty of other friends, whereas I had none, but I think the catalyst was the arrival of another new girl (not the first since she had joined, nor a particularly unusual new girl); those two quickly became friends. And when I say that she "abandoned the relationship," this was a pretty epic change. It went from borrowing my sled at recess to bullying me so badly that I would hide underneath the playground equipment while she screamed at me. She would even go to playground supervisors and tell them awful things I had supposedly done (not a single one of which I had done and, furthermore, not ones I would even have had any concept of doing) while I hid and, because of my mostly-Asperger's-induced unpopularity with the school staff, they tended to believe her over me no matter what she said.
However, that was just one girl.
All of the other friends I've had until very recently have been male, and those friendships have all been easier. None has ended in anything other than simple moving on - either to another school, to another city, or just generally. There have been no hard feelings. And at the moment, most of the people I consider friends are male. Now that they're all adults, perhaps it's time to give girls another chance.