I just wanted to share my experience in case it helps others. I was having problems staying consistently connected to the internet with Wii, even though I have no problems on my laptop. I was also experiencing extremely slow download times - which was a real pain.
Here's what I did, and it really helped a lot:
Per Nintendo's support website, try changing the channel of your wireless router. Look up the owner's manual for your router online (if you don't have it.) In it, there should be a Wireless Settings area that gives you an IP address to direct your browser to. (I recommend plugging your PC in to your router via CAT-5 cable before you make any changes to these settings.)
Direct your browser to said IP address. Find the Wireless Settings section, usually near Encryption Settings. You should see a channel setting. Default is channel 6 - change it to 1 or 11. I also recommend setting up data encryption keys if you don't have them already - esp if you are buying wii points directly on the wii.
Changing the channel setting will distinguish your wireless signal from other wireless signals in the area. I don't know about you - but there are about 7 wireless networks my Wii picks up!! That causes lots of interference and confuses the connection. Changing my wireless channel to 11 made DRASTIC improvements.
Hope this helps anyone who is having the same problems i did.