Just to say that I have the same problem and it's more than just frustrating. I like Apple's products but Apple is undoubtedly a pain in the butt when it comes to both meeting key user requirements and/or solving Apple software bugs / problems. Seems to me Apple should have not made iOS 8 available for earlier iPad IPhone models if they can't meet the spec.
That said I finally found a solution that worked for me: -
- Select Settings
- Select General
- Select Reset
- Select Erase All Content and Settings
IOS 8.1 (assuming you have the latest set up should remain operational)
You can then start all over again i.e. iOS8 should take you through the start up routine and then you can use the App Store App to re-load purchased Apps.
If to you iCloud you should then be able to get contacts etc. sync as well.
I am no Apple specialist and I make no guarantees with respect to data, calendars etc. but I did do the reset with my iPad 2 and it now seems to be working fine. I took this approach after seeing various other comments about doing a complete reset that seemed to have worked for others too. It's all a bit of a pain but once you get around to doing it, it is not really that much of a hassle. At least for the apps I use, some of which sync with other devices it was fairly painless and the loss of frustration has been a bit boost!!