The others SIMS disconnect too, but only after put in the PIN code. Before enter the pin code I CAN use AT commands without problems (without limit of time).
I think you are going to find this is a power supply problem. I had the exact same problem when I was prototyping a SimCom GSM module.
How are you powering the device? You're power supply must be able to supply at least 2 amps so it can't be powered through USB. What's happening is the modem is trying to register to the network and you're power supply is dropping out causing it to shut down.