Call waiting tones but no way to accept the call

The strangest thing has been happening for about the last week now.

While on a phone call with someone and in a place with strong signal, I will receive a call-waiting tone, but when I look at the screen there is no indication of an incoming call.

So, I press the green "talk" button and get the prompt to start a new call, instead of a "Call 1 Holding/Call 2 Active" indication like I normally do. But when I press the back button I see my current call info for only about a second and then it says "disconnected" but the person is still talking to me. At this point I am looking at my home screen with no indication of an active call and continuing to talk to the first caller.

20-30 seconds later I get a new voicemail notification and the call that I was originally on finally drops completely.

I know this sounds crazy, but is there anyone else who has had this happen?