Very useful post, nice to have all the information in one place. I had a lot of trouble with this and I didn't understand what I was doing wrong but it turns out I was flashing the WRONG rom. Make sure the ROM you download in step 3 is called "LT26w (Xperia acro S)_6.1.A.2.55_Version" and is ONLY 11MB
. I was flashing a ROM that was 400MB so when I rebooted my phone I lost CWM and root.
When I flashed the correct ROM, my phone restarted and I still had CWM. I then proceeded with installing the zip file through CWM and it worked! This only takes less than 5 minutes (if you're doing it correctly) and when your phone restarts you should still have all of your data (if you didn't wipe).
Hope this solves the problem of people losing CWM when they flash the ROM - press thanks if I helped!
P.S. you will have both Superuser and Supersu if you followed the method in the OP. If you want to keep SuperSU you can go to System/App and delete the superuser.apk. If you want to keep Superuser you can open the SuperSU app and go to settings and there is a place to switch SU apps, or you can uninstall the SuperSU app from your phone completely.
Sony Xperia Acro S
Stock Jelly Bean, Android Version 4.12, build number 6.2.B.1.96 with root and CWM
Press thanks if I helped you - it's free!