I have recently managed to root my Padfone 1 (prime) with JB without losing apps data and apps settings. I want to share how I have done that and which guides I have used.

Unfortunately there is no possibility to root Asus JB android version so you have to downgrade to Ice Cream Sandwich (ICS) and this cause losing all data stored in Padfone's internal memory. Luckily there is great App Backup preinstalled by Asus in Padfone.
Note: If you had already rooted your PadFone on ICS but lost your root after update to JB then there's an option to restore it. See this thenrz's guide on xda-developers.

  1. First of all backup all photos, music, videos and other personal files stored in padfone's internal memory. SD Card will stay untouched so you can copy your data on it but it is always safer to copy the backup to your PC.
  2. Then we can backup applications. Run App Backup on Padfone. In the top right corner tap "Data only" and choose "Data and APP" option. This is very important to switch this option. If you don't do that then you will have to install all applications manually after rooting. Select all applications you want to backup. In the left bottom corner press the circular arrow. Make sure that "Copy backup file to" is set to some place on your MicroSD and press ok. After the backup process is completed you may want to copy the backup file to your PC to make sure it is safe.
  3. We are now ready to downgrade to ICS. To do this please follow this Marc Schattorie's guide on padfoneclub. I have used international WW_PadFone-user- from "Download official full firmware packages here (Removed from the Asus website)" section. Put it into SD Card and follow "How to install?" steps.

    How to install?
    First, make sure you have the firmware (*.zip) file in the root of an external SD card.
    Also, make sure that the Padfone is fully charged, and connected to a power source.
    If you're downgrading or changing the firmware region by using a full firmware package, we would recommend using the wipe feature before you apply the update.

    1. Undock the Padfone.
    2. Power off the Padfone.
    3. Hold down the volume down button, keep holding it, and press the power button. Now you will enter the first menu.
    4. Press the power button to enter "download mode".
    5. Select the second option to install from an external SD card.
    6. Wait for the installation to complete, depending on the update, your device will reboot automatically, or you
    have to select the reboot option manually when it appears.
  4. When we are on ICS we can use this sparkym3's guide on xda-developers to obtain the root.
  5. After rooting we must save the root that we could restore it after updating to the newest android version. To do this we will use Voodoo OTA Rootkeeper application. Download it from Google Play store and run it. To save the root tap the "Protect root" button.
  6. Now we can use standard android update system to update it to the newest version. Go to settings -> about padfone -> system firmware update and tap the "Check Update" button. Android should find and proceed with the newest update.
  7. Now the last two things. After android is again updated to JB we must use the OTA Rootkeeper to restore the root. Lunch it and tap the "Restore root" button. Restart your Padfone and again run OTA Rootkeeper. You should now see all status positions checked. You have root on JB!
  8. Go to App Backup. In the top left corner tap "Backup List" and choose "Restore List" option. Tap on your backup and tap OK. After App Backup finishes the restore process you should see all your applications with all your settings and data.