Your comments

Because this problem happened predominantly with TextTastic under iOS 7, when it continued to happen with my switch to 8, I came here looking for an answer. 
As I have used 8 more, though, I saw the same behaviour in other apps. Turns out that the real problem was at the OS level. A reset  of all settings proved to be the fix. 
Sorry to have sent you looking for a problem that didn't exist with your excellent software.
Happened with both iOS 7 and 8.