How far away is your Wii from your router? That could affect the connection based on the amount of servers.
Also, I looked up the error code and found this.
http://www.nintendo.com/consumer/wfc/en_na/ds/results.jsp?error_code=51330&system=Wii&locale=en_US
Hope this helps, since streaming services on Wii and Wii U are convenient.