Is there any way you can install it to SD card or something? From there you could just copy the APK from the SD card and save it somewhere. If you not, you might be able to find the .apk for it somewhere on your phone's storage (you don't have to be rooted to screw around your phone storage, just to view certain portions of it. Sometimes the app might have additional data outside that hidden portion (root) and you'll be able to copy and paste the .apk). It won't save your data, but at least you'll have the app...