I'm having the exact same issue. I'm with Verizon and they (along with Apple) have no idea what could be causing this. All I can tell you is to contact your provider OR Apple and see about getting a replacement. That's what they're doing for me and I'm hoping it'll solve the problem but I don't think it will.
I am having this issue too. I have replaced the SIM card twice and Apple replaced my device. Two days later I was missing calls.... no notification at all only knew they called when they left a voicemail. I have verizon and have called at least once a month since April to resolve the issue and still having problems. If you find a solution to this problem please pass it along. Thanks.