I have solved this issue by implementing the following:
- Rewrote my tableview controller as a standard ViewController, not a TableViewController
- Added a tableview to the ViewController and a separate "contentWrapper" view.
- The content wrapper consists of the example shown here: https://github.com/datwelk/RDRStickyKeyboardView
I'm still not sure what in iOS 7.1 caused this issue, but using the RDRStickyKeyboardView works great and solved all of my issues.
I've read that tableviews shouldn't be parents of other views, so this solution also works well for good coding practice.