I experienced the exact same thing awhile back. On a hunch, I deleted all of the downloaded missions and the original PonyVsPony missions suddenly started working again. I don't pretend to know how the game works, but it seems to me that when you start the Offline mode, the game loads "something" from each of the Practice missions that you have downloaded. It is my belief that one of first missions created by somebody had some sort of fatal error that is causing the entire Offline Practice mode to function incorrectly.
I could be completely wrong though.
My advice is to pull all of the downloaded missions out of your folder, then add the ones you know you want back in one at a time, restarting the game and testing each mission as you go. When everything stops working after adding one, you have found the culprit.
I just got rid of them all and now make it a point not to add any of the older missions. Those early creations are more likely to be buggy. I haven't had any problem since.