Hi Matt,
That seems to be some variant of that problem, when tapping in the search icon the keyboard shows up and I can't type anything in the input filed.
There's a plugin for Cordova to use WKWebView but that will only help with devices running iOS8, leaving older devices unsupported.
I was testing pdf.js on the same iPad and they seem to have solved that issue since the search field in their viewer doesn't show that problem.
We'll try to see how they managed to get it working.
Regards
Vlad