This is happening to me as well. My Droid doesn't ring and several hours later, it vibrates for voice mails. When I check them, they are several hours old. I don't have any notification of missed calls nor do I have it in my call log. The people tell me it rings 4/5 times and then they get my voice mail. I've had a Blackberry for 4 years and never had this problem at my home...which I work from home. This has never happened until I got my Droid. I'm on my 3rd one and I'm taking it back and going to get a new Blackberry...I'm tired of all the problems of the Droid.
This isn't the issue...I know that option is there, but it's sporadic with different numbers. Some how the phone goes to some sort of sleep mode. I found that I don't even get text messages when it goes into the "hidden" sleep mode. I will call to check my voice mails (no notification that I have one, just doing it to use the phone) then I'll get several text messages and voice messages at once. It seems when I use the phone, it wakes back up and all the notifications are sent at once. Don't call Verizon...nothing but morons work there. If I have to hear them ask me to make sure my volume is turned up, I'm going to throw my phone towards their forehead. My other Verizon phone, Blackberry, is not doing this. So it's not a signal issue...I always have full signal with 3G.I had this problem. Be sure to check the options for whichever contact's call that you're not receiving. There is an option to send their calls straight to voicemail. Make sure the option is unchecked. I'm not sure how or why, but this option seemed to have turned itself on.
Hope this helps!