I've been having difficulties too the 3G and signal just went and said searching for around 6-7 hours then comes back on by itself, I tried everything resetting the iPad, removing and replacing the sim card, and resetting network connections in general settings. Nothing worked and it appeared to be three mobile. But it is happening more frequently lately. I'm in Lincolnshire area if that helps. Usually I have a great full signal of 5 bars like now but I was sat in this exact same spot when the network went. I'm not sure what else it can be.
I've read on other threads lately people are having to reset their iPad 3's after connecting to a wifi connection to get it back on?