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There might be an issue with your SIM card, but do repair your phone with either PCC or SUS and double check the APN settings with your carrier or google them
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before you repair your phone id suggest getting your internet settings from your operator again just to make sure the access points are configured properly.
This might be the first step. go to settings > more> internet settings.
See if this helps. Also make sure mobile data in that pannel is turned on.
If the phone is having an issue connecting to the network, either its the network itself or your internet settings.
My last phone, Xperia Arc had the same issue, but im very sure it was the network, I would spend most the day at work on WiFi then I would head home, when it switches over, sometimes it wouldnt transfer data on the network.
Flight mode reset the network and it worked fine, but sometimes I lost connected for almost an hour.
But as a past consultant for a service provider, get the settings from your provider first 