Q:

Unable to load the service index for source https://api.nuget.org/v3/index.json in VS2017?

I am getting This error:

[nuget.org] Unable to load the service index for source
  https://api.nuget.org/v3/index.json.   An error occurred while sending
  the request.   Unable to connect to the remote server   A connection
  attempt failed because the connected party did not properly respond
  after a period of time, or established connection failed because
  connected host has failed to respond 185.82.212.95:8080

A:

I was having same issue in VS 2017. You would need to enable proxy settings for VS, so that it can use existing IE proxy to reach out internet. This is especially useful, for those users, who uses office laptops and proxy settings are managed by group policies and IE settings get updated automatically. It would have been great if there was an option within VS IDE itself to add proxy just like Eclipse IDE has.
Solution

Go to your Visual Studio install location as below -

C:\Program Files (x86)\Microsoft Visual
  Studio\2017\Professional\Common7\IDE

Open devenv.exe.config file as an Administrator. 

Add defaultProxy tags as below, within the existing system.net tag -
<system.net>
    <defaultProxy enabled="true" useDefaultCredentials="true">
        <proxy usesystemdefault="true" bypassonlocal="true" />
    </defaultProxy>
  <settings>
    <ipv6 enabled="true"/>
  </settings>
</system.net>

Restart VS.

A:

TLDR ;)
FYI: the same issue is still happening for VS 2019 Version 16.6.3.

Ok, let's get started to fix this issue :)
First, you need to navigate the Visual Studio instance and for that do the following:

Open Properties on VS shortcut and then click on "Open File Location"

Edit as administrator the devenv.exe.config with Notepad++ or other editors you prefer:

Navigate to the end of a file and check if you don't have <defaultProxy>... section:

Make sure to add following inside <system.net>:

   <defaultProxy enabled="true" useDefaultCredentials="true">
      <proxy usesystemdefault="true" bypassonlocal="true" />
   </defaultProxy>

The final result should be like this:

A few notes:

If you have several Visual Studio instances then make sure you edited  devenv.exe.config for each one.
Sometimes after VS updates, these files content can reset. So a good hint here is that once you Update Visual Studio instance, then go and check the .exe.config file.

Update:
Btw, the same kind of approach work for many other applications, for example, check this post.

