Gmail push notifications very erratic on iPhone and iPad

Question

iPhone 4S
iOS 6.1.2
iPad 2
iOS 6.1.2
The push notifications on my iPhone and iPad have become very erratic but ONLY for my gmail account.  My work exchange account is working fine, in fact flawless.
Symptons:  I will receive an email that I can clearly see on gmail.com, but will wait for my iPhone and iPad to notify me and nothing.  I'l wait several minutes and still nothing.  I wake my iphone and check mail and have to manually pull down to refresh my email.  It's not all the time though, it's very sporadic.  For instance, if I wait long enough they will eventually show on my lock screen, but it can be several minutes to a half hour or more.
I only noticed this the past few days and I'm almost positive that I just upgraded both my iPad and iPhone to 6.1.2 just last week.  I am not sure if I can sum this up to "happening right after the upgrade to 6.1.2" or not.  However, it does seem to be a strong coincidence that I just upgraded and now I'm having the problem.
I have both my iPhone and iPad notifications set up the same way for both my email accounts and both have always worked fine and both have become erratic within the last few days.  I have not changed any settings.  I notice this both when I'm on cellular and when I'm home on my wifi network.
Is this something others are experiencing?  Strange that it's both my iPhone and iPad and no settings have changed.
Thanks all for any help you can offer.

Answer 1

I'm not sure if any of you use the gmail exchange support which WAS the only way you could sync email and calendar events and get push notifications for years.  Well it's going away, actually it's gone for new sync users.  For instance, you can not set up a new phone the way I have my phone set up if you are setting up a new sync account.  However, google's article...
http://support.google.com/a/bin/answer.py?hl=en-uk&hlrm=en&answer=2716936
...clearly states that if you were an existing sync customer, you should have no problems.  Well, I guess they are sort of trying to "push" people to the new CardDAV.  I guess I'll bite and try it out tonight.  I am a very old google sync user (iphone 3G, 4 and 4S) and have not changed anything, so from this article I should be fine.  Well, I'm not.
I'll definitely try the "new" way and let you all know tonight (or tomorrow morning) how it's going.
Thanks again for the replies.
Support for exchange active sync was dropped by Google for free accounts on Jan 30 of 2013. Apple was prepared for that since November of last year, you can check date on that article.
http://support.apple.com/kb/HT4872?viewlocale=en_US
Since Gmail still using Card Dav protocol, it allows new devices to sync Contacts. Google mail account takes care of emails and calendars sync by itself. It does have to do with push (you dead on), cause exchange supports push on whole other level, but it has nothing to do with your case. The information that I gave in my first post still stands. It looks like you think you know more then all people that responded to you, but (sorry, still feeling entitled to my humble opinion) you will see your push fixed by itself. Even funnier if you will make some change and it will coincide with google server back online. You will come here and provide us with your "fix".
Perhaps it will be something like "I just changed show emails from 100 to 200."
@applenascent.
The way it works is simple. We do not realize, but google server actually knows what device is connecting to their server to pick mail. I had to replace my wife's ipad on Feb 7. Even when I restored from the icloud back up that for all intents and purposes made that ipad very similar - the account was still there, but simple gmail without exchange. Deleting account and re adding as exchange didn't provide solution. It just showed up as gmail. They even changed server name from m.google.com to google.com.
BTW it is quite possible that aTanasi's trick will fix the problem. I had to start running yahoo and gmail apps running on the background. I do not use them, but if there is a problem with account, like security kicks in harder, app is more capable to address that issue and informs me of what is wrong. I still find native mail app more pleasant, but thanks and credit to aTanasi.