This article contains the troubleshooting steps for issues pairing the Remote app:
This worked for me, from another user:
I have an Airport Extreme with two networks: A closed home network, and a guest network for guests with guest network priviledges. For whatever reason, my iOS devices will sometimes switch to the guest network, which does not allow for Remote use. I'll troubleshoot the heck out of not being able to see my iTunes library until I eventually stumble onto the fact that I am on the wrong network. Make sure you check that your wireless connection is on the network associated with the iTunes/Home Sharing setup as a part of your troubleshooting.