E-Mail notifications only work for first e-mail account (GMail)? Currently I finally - way too late - noticed that still in iOS 6, the Apple Mail app is not sending me push notifications - or any notifications for that matter - for any of my e-mail accounts except the first one, which happens to be my GMail account.

The other ones (of 6 total) are: Another GMail account, a Nate(.com) &amp; Daum(.net) account and two domain names I bought (one via GoogleApps, the other not).

My settings are: Push and "Fetch every 15 minutes", with Fetch activated for all email accounts named above.

So as I get no notifications (and thus today missed an important e-mail in the afternoon, even though I kept an eye on my phone), I wonder how to troubleshoot this?

Finally I wonder why "push" is still not a reality? I mean in all my settings there is no "push" option, for whatever of the above accounts I use. Is "push" only possible when you have a Blackberry or Sharepoint or sth. ?
I know push works for iCloud email accounts (@me.com), but as for the other ones, I'm not positive.

You can configure your email notifications by tapping Settings > Notifications > Mail. After you are there, you will notice a list of email accounts. It appears that you have to customize each individual mail account separately. Tap on a email account, and you can configure it to alert you exactly the way you desire to be notified. 

You can also use VIPs (under the list of email accounts mentioned above, or accessed by by tapping the arrow to the right of the VIP mailbox just under All Inboxes in the Mail app) to customize notifications depending on if particular senders are consistently urgent.