When Evernote hangs, it crashes (actually I think iOS kills it judging by the log). However, when I reopen the app, the search field is still populated, so it still winds up hung on the previous search, so the search field *can't* be cleared.
However, It seems if I can force kill the app from the iOS app switcher *before* iOS kills it, then when it restarts the search field is empty.
Unfortunately searching for a note, switching to Safari/Mail and switching back to the note causing the hang/crash loop seems to be something I tend to do pretty often.