I have a same problem with my GS 3 mini and finally I found out how to solve.
Do you have Go Power Master installed in your device and you set it to your device's administrator? If yes you must uninstall Go Power Master or recheck the device's administrator box so Go Power Master isn't your device administrator anymore.
Enable your mobile data and it won't automatically disable within 2-4 sec anymore.
Maybe this will be helpful.