I've been experiencing the same issues since I upgraded to 6.1.2, and it's been very random.
One thing I discovered by accident,... if I'm replying to an existing thread when the problem starts, the message may take an hour or so (if ever) to be delivered by normal SMS.
But,... If I delete the existing thread with the person I'm having issues with and start a NEW message with that contact the iMessage works perfectly!! (shows Delivered, & I can see when the person is replying back from their iPhone)
Obviously this is a hassle! But it's a Band-Aide fix to make sure the message goes through timely. Still want a proper fix & I didn't see this in this discussion (unless I missed it), so I thought I'd pass it along.
I'm having the same problem. It has not worked even if I start a new thread. The worse part is I am overseas and was relying on my iMessage to be working. I should not have upgraded the iOS. (Other phones which are running the old iOS 6.0.1 is working ok). It appears that I am not receiving my iMessage to my phone even if it is said "delivered" which is very deceiving to people sending me messages.