This sound like a cross domain issue. That is why ajax is not working. A solution would be to find a plugin that allows for JSONP calls. If you can not find one that fits what you need, let me know I can fairly easily add it to the appMobiDev plugin.
If I can ask, what are you looking to use Ajax for in your games? Is it for saving scores, game data, etc..? If so, checkout our playMobi plugin. That is our cloud service for things like leaderboards, badges, game data, etc...
Again, just let me know if you can't find a plugin to fit your needs. I'll be more then happy to help out and add jsonp actions to he appmobiDev plugin.