Apple Mail Client stops working abruptly and randomly with Gmail

Using iPhone 6.

On IOS 8.4

I add my Gmail account, either by manually entering the IMAP information, or by simply pushing the "Google" account button.

Everything works great, all the emails sync, I get the flagged ones, the drafts etc. It is working beautifully and continues to do so for an inconsistent amount of time. Sometimes 2 weeks, sometimes a week, sometimes 3 days...

Lately its stopping twice a week, in other words, getting worse.

The client just stops working, usually over night, when I have left the office. I typically respond to my emails right away, and should it be something more dire, I would flag it. As to not confuse the new emails that are coming in. So I usually do not have any unread emails in my inbox, unless well, they are unread.

So, on goes my evening and my phone has no un-read emails, and thus I assume I have not received any..... Well I go to the office to a myriad of unread emails that just have not gone to my phone.

I pull down on the screen on my iphone to "refresh" my emails and it doesnt seem to work. It says checking mail continuously. So I go to delete the account (By the way, this is the only consistent part of this whole process... the complete lack of the phones ability to connect to gmail) and the deleting grey box appears and just spins and spins and spins, until I must shut off the phone and restart it.

Just so I can re-do this entire thing again... and once I do, it does work beautifully and properly..... for 3 days or so.

I have read that this is a consistent problem, and upon a phone call to Apple Support they have acknowledged the issue...