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It sounds like this is a network related problem. Do you have the possibility to try with another SIM card in your phone? You could also talk to your network provider to see if they can find any error.
I have this problem too & I've tried other SIM cards in this phone, my SIM card that works perfectly in my Xperia S, I've reset my Z1 Compact to factory setting & also I've used Sony Companion too to try & repair it but nothing seems to work.
In that case I suggest that you talk with your service provider. Perhaps if they send you a new SIM card it will work better.