Are you on VPS or shared hosting? It sounds like you are running out or memory (RAM) on the server.
Or possibly what may be happening is a conflict with another plugin or possibly the theme as you said. I would first try switching to the default 2011 theme. If that is working, then you will know it is your theme. If it is not working after that, it may be a plugin conflict and you can try deactivating all your plugins and turning them on one by one and see which one breaks it.