Same problem here
I've been having the same problem since my Xperia Z3 Compact received the Over-the-Air update to Lollipop. I have T-Mobile too, and they had me re-enter the APN settings, to no avail. The problem persists. I will not do a Repair because I don't want a factory reset (for various obvious reasons). Plus, reading this thread tells me that a Repair won't fix the problem. Even through the two of us both have T-Mobile, I think this is a coincidence and this problem has nothing to do with the carrier. This is purely a bug in the Sony edition of the Lollipop O/S.