The 4s records video as MPEG4/AVC (H.264)/1080p/30fps in a .mov filetype. Final Cut Express is NOT designed to edit this kind of video. You need to convert the 4s video clips to QuickTime/Apple Intermediate Codec/1080i before importing them into FCE. You can use MPEG Streamclip to do the conversion. In FCE you also need to select a matching Easy Setup (should be AVCHD Apple Intermediate Codec 1920x1080i60 for converted 4s clips) and create a new Sequence to edit your video. This should eliminate the constant re-rendering problem.
ps. Final Cut Express was discontinued in 2011 even before OS X Lion was released. It is no longer supported by Apple and there is no guarantee it will run properly on Yosemite. Just so you know. Final Cut Pro X is the currently supported app.