You might try installing an updated firmware version for your router if one is available on the manufacturer's website, and/or checking the firewall settings for it and increasing the number of allowed connections/sessions/"incomplete packets" or similar options.
Actually, another thing to try would be to lower the number of connections Opera tries to use.
To do this, go to Tools->Preferences in the top menu, then go to the Advanced tab at the top of the window that pops up. Choose Network from the left menu, and then lower the values for "Max connections to a server" and "Max total connections".