I am having a similar problem now as well. It started yesterday, most of my incoming calls never show up to my phone. But when they leave a voicemail, I do get a notification for that. Text messages and internet also work flawlessly.
You might be on to something about how it won't receive a call when in sleep mode. Since my iphone is in sleep mode most of the time, most calls aren't making it through to my iPhone. Gonna try to test this out and call my phone when it is awake and on. Then call back when it is in sleep mode and see if this makes any difference.
I called iPhone tech support today and she had me reset my iphone and she tried calling my iphone and it never rang. So, she had me turn the Airplane Mode on and off a few times. Once I did that she tried calling and it worked. However, since then half of my incoming calls haven't made it through to my iphone.