yes, now i just sync it everytime i power-on the AC adaptor.
if i dont power-off my AC adaptor, and let's say i go to Wii Home, my Wii fit automatically power-off (blue light off) - which is normal.
At this point, to enable again, i simply press the power on wii as you mention and it works again (as usual).
the only problem is when i really shut off the power supply to my wii and then it seems like it just forget everything.
i did thought of the battery and try a new one to confirm. it looks the same as well.