Most of the time, the data icon is still visible in the status bar, but no pages load. The status bar data toggle off / on gets it connected again. Sometimes however, the data icon goes away and only a reboot or toggling flight mode brings it back.
I'm running Ditto Note 3 (KK), but had similar issues on previous custom roms and stock 4.3. I don't remember having any problems with the original Jelly Bean. A friend also has the same issues which started around the same time, on stock unrooted Samsung 4.3. We're both on Orange (UK).
Is this a software issue, or could it be anything to do with the SIM card?