i had the same prob and this workaround worker for me! thanks. only happened after 6.1.3 upgrade on my ipad 3, was no issue after same upgrade on my iphone 5. both my apple mail and gmail apps didnt work, so clearly something wrong bw ios and gmail there, dont know who's fault it is, but apple getting the blame, which is probably fair. if i wanted an os that needed a lot of manual tweaking i would already be on android, after this and some other issues ive had, i'm headed that direction more and more.
This is also what I had to do to resolve my battery drain issue.
I have an iPhone 5 and had the following email accounts: Gmail (x1), Yahoo (x1), Exchange (x1-really a gmail account).
After the 6.1.3 "upgrade", I noticed my phone overheating in my pocket at work, where we don't have accessible wi-fi. The phone heated up and the battery life dropped very quickly. I would arrive at work with near 100% charge, and 2 hours in the office it was down to the 45-48% range with very little usage. I used to go all day and still have 60-70%+ at night before bed.
I did a complete restore as new and backup using iTunes and that didn't help. I read about the issues with Exchange, so I deleted all the email accounts and recreated them as Gmail (x2) and Yahoo (x1). I was still having the issue. Then I read about the issues with Gmail, but I only deleted 1 of the gmail accounts and recreated it as an "Other" email account as mentioned by goBlue2003. So far, this has resolved my glitchy email and the massive battery drain. I still have my phone on Fetch rather than Push, but in the past few hours the battery has only dropped 2%.
I have this problem but none of the proposed solutions work for me. I cannot open my mail and calendar porefernces to remove the gmail account. I cannot even seem to access my icloud account to restore a backup. One of my problems seems to be that the "settings" app is broken. My iPhone 5 is F'd.
No appointments avaiable at the Apple store tonight so I guess I will have to go tomorrow on my birthday instead. Boo Apple.
Any suggestions? I can try to back up to an iMac and then restore from there?
It happenned the same to me and I have and iPhone 4S. I tried all the suggestions many people suggested before and nothing changed. The only thing missed to make it was restore the iphone with the hope I had the same iPhone I bought (I mean with the original iOS).
However for my surprise I got the iPhone I bought but with iOS 6.1.3!!!!!!!!! OMG I couldn't believe it, but when i set up my GMail e-mail accounts all was fine, everything ran OK.
The only bad thing about this was the time I spent making backups of my pictures, files associated with some apps, doing "print screen" to each screen of my apps and the worst was restoring all these pictures, files and the apps in the same order in my restoring iPhone..... in total 6 hours........ dissapointing but I solved the problem.
I hope this solution helps to all of you.