Simplicity Studio accesses the following sites during online installation/update.
 3_x_public
 3_x_eclipse


If access to the above site is blocked by a firewall, installation/update will fail. In this case, you can bypass the firewall and install/update by setting the proxy properly.

When installing, press the Cancel button in the Add/Remove packages dialog to exit once, and enter the proxy information in Setting (gear icon) → General → Network Connections.
When updating, please set in Settings → General → Network Connections as well. If you are not sure what information to enter, please contact your company's IT administration.
Also check out the Silicon Labs community site.