I'd wager that it's the encryption key you need to configure on the Wii.
Agreed, though it's strange the AP isn't always visible and fluctuates between good signal and shit. Do you have WEP/WPA enabled on the router?
Anyway my suggestions:
1. Configure the connection up manually on the wii. IIRC there are multiple pages of information for the wireless setup which isn't 't obvious from the first screen. Check this out for a typical experience!
http://www.wandering.net/2007/03/05/how-to-setup-wifi-for-the-wii-if-you-have/Still no joy/flakey breaky connection?
Does your wireless network work OK in the same location as the WII on another device (say laptop). If not
1. You are getting interference of some kind. Try a different WIFI channel, usually configured on the router (switch from 'auto' to a specific channel. You can use trial and error OR download netstumbler (
www.NetStumbler.comdownloads/) onto a laptop, put it neer the wii and see which channels are already in use.
2. You are genuinely out of range. Unlikely if you sometimes get strong signal. Temporarily resite Wii closer to router to get it working ?
3. Incompatibility between router and wii. Probably not.
4. Your wii is fucked. Probably not though.