Almost destroyed my s4 out of frustration. I first thought it was my note2,then had the same issues on my s4 so I got a now sim. Issues seemed to go away for 2 or so months until now. Restart didn't restore connection.
Issues seemed to come and go but were always just on my device. Now I know though, can't wait for my contract to run out next month...
*** thing is, try Google'ing what is happening and all results pretty much point to grey import phones with dodgy unlocks or software updates that have stripped the IMEI number from the phone.
I suggest logging a ticket so that we can get some numbers behind this.