I had a problem with Logic Remote when first came out, and tracked it down to an interaction with a 3rd party iPad logic control app. I think it was touchosc, but I'm not 100% sure. I had to make sure that Logic "forgot" about its linking to the third party app. This was quite a while ago, so I can't remember the details. Just wanted to get you pointed in the right direction.
Sounds like you may have done this already, but about the only other suggestion I can offer is to follow these steps as outlined in the Apple support article: http://support.apple.com/kb/TS5172
They specify the following sequence:
Quit the Logic Remote app if it is running.
Open Logic Pro X.
Choose Logic Pro X > Control Surfaces > Setup.
In the Setup window, delete any Touch OSC devices listed.
If there is an existing Logic Remote in the setup window, delete it.
Launch the Logic Remote app and connect to the Mac.
Accept the connection when prompted in Logic Pro X.
Note that they delete Logic Remote from LogicX's setup also, and then reconnect it. I have a vague recollection that there was a little twist like that necessary to solve my problem. There is also a link in that support article to a possible interaction with OSX's firewall settings.