iMessage always eats my messages. Both directions.
It’s been broken since I set up my first iPad,
which always gets all of my messages if it is logged in to iMessage.

If I turn off iMessage, Apple users cannot message me, but they get my SMS messages.
I turned it off before moving off of AT&T, but it was mostly broken there too.

I have wiped and reinstalled.
I have moved to a new device.
No AppleCare, so I’m not calling in.

My solution came from complaints about this happening on iOS 7.
The fix appears to be a subset of http://support.apple.com/kb/ts2755.

The summary of this fix, which should fix 99% of any iMessage problems:
* Settings -> Disable Facetime and iMessage on all devices
* Settings -> General -> Reset -> Network on all devices.
* Wait for reboot to finish
* Re-add any WiFi networks as needed.
* On the iPhone first, turn on iMessage. Wait for it to register.
* Turn on Facetime
* On other devices, one at a time, turn on iMessage, then Facetime.

Now, iMessage is working working better than ever.
1) I sent a message from my phone, and I see it on my iPad as having been sent as well. I never had that.

2) I sent one to my son who’s network is turned off in the evenings. My phone said it was sent iMessage. After 2 mins, it updated and said it was sent via SMS.

Neither of these have ever happened for me, so it’s all better than fixed. yAy!