(IDNY but the video blackouts in the beginning. Just forward it manually with your mouse and it'd show up.)
It's physically impossible to sing live all the time given the frequency of live performances BoA has to give.
Just like us, she also gets sick from time to time and suffers from sore throat, cough, flu, etc. So, sometimes she lip synchs.
However, fans who don't know her well forget that BoA is an amazing live singer. Recall the New York documentary where it shows a glimpse of how BoA trains to sing live. She runs around in circles while singing and the trainer was very strict with her not to slow down.
This performance is live. She did a great job and I admire how her voice is so steady even while dancing. That is a very difficult skill to master. I can't even talk when I'm dancing. She truly is a professional.
"If you want to be twice as good, practise ten times as hard."