You're still a bladesinger.
The restriction is phrased as follows:
Only elves and half-elves can choose the bladesinger arcane tradition. In the world of Faerûn, elves closely guard the secrets of bladesinging.
RAW, you only have to be an elf when you choose the arcane tradition, so becoming a non-elf after gaining this class wouldn't matter.
RAIInterpreting more freely, the phrase "elves closely guard the secrets of bladesinging" suggests that the reason for the restriction is that elves don't share their knowledge with outsiders. However, if you are an elf turned human after a Reincarnation spell, you would presumably still know your elf family, friends etc, so you probably wouldn't be considered an "outsider".