iMessage not working between two specific devices iMessage works perfectly between my iPhone and my iPad. It works perfectly between my iPhone and my girlfriend's iPod touch. But it does not work at all between my iPad and my girlfriend's iPod touch.

All three devices can use iMessage just fine with other devices. The only issue is when we try to communicate between iPad and iPod, and it's really infuriating. Any ideas?
First, check the destination address. On your iPad: open Messages, then open the message thread that's not working. Tap the "Contact" button (top right), then the "info" button (i). The destination address will be highlighted blue.

Next, make sure the destination address is configured on the receiving device. On the iPod: Settings &rarr; Messages &rarr; Send &amp; Receive. If the destination address is missing, add it here.

And while you're at it, check the FaceTime settings, too: it works in a similar way.