FrontlineSMS is only able to automatically process incoming and outgoing messages when the device you are using (phone or modem) is connected to the software. If it is disconnected for a period of time incoming messages will be held by the phone (or the operator message centre if the phone is off), and when reconnected the software will pick the messages up. FrontlineSMS will still then trigger any actions you have set on an incoming text, for example a keyword trigger. No messages should be lost, unless you manually delete them from the phone before reconnecting it.