I suppose your problem is of the same origin as I had with gsm modems.
Sending a command you get an acknowledgement from the device, then send the next command, get ack, etc, etc. Soon or later the device hangs up.
The key is the interpretation of the acknowledgement.
You may think the acknowledgement means the command is accepted AND executed. However - at least at ALL gsm modems I know - it means no more but the command was accepted and INTERPRETED - but not executed. In case of time consuming commands you send your next command during previous command is being executed. You do it because you may think acknowledgement means the command is done - but it is not true.
The device may or may not buffering cumulative commands, but soon or later the device runs out of resources and hangs up.
I have no experience with device you use but the phenomena seems to be the same.