Go download an OTR client for iOS, like cryptocat and notice how it pings you after 10 minutes that you have to re-open the app to keep on receiving messages! It's because iOS does not allow you to keep an app running in the background indefinately for battery reasons. This is required for the XMPP / OTR model to work.
You need a protocol of some sort that would work properly with mobile, and I think textsecure is it.