3DS e-shop still won't connect for me. Hopefully it is just server load rather than any real issue.
Are you perhaps the experiencing the dreaded 007-2100 error? It's pretty common, but there are some easy fixes that usually work. You could try changing the DNS setting.
On your 3DS:
1. Go to settings
2. Choose Internet Options
3. Choose Connection Settings
4. Choose your current connection and change settings
5. Choose DNS (second screen)
6. Select No and go to detailed set-up
7. Primary DNS 008.008.008.008, Secondary DNS 008.008.004.004.
8. Test your connection. If it functions, try accessing the eShop
The 007-2100 might also be related to the latest update (which you probably just installed, because that's the one that introduced MiiVerse on the 3DS), in which case you'll just have to wait and see, I guess. Nintendo is working on it.