Obviously, no device can receive messages when it is switched off - whether it’s a phone, an FXT, or whatever!
Similarly when a device - any device - has insufficient signal.
But the message is not lost - it is held by the network until it “sees” the device again and can deliver it.
But see: SL8090 Synchronisation indication for SMS retreival - #5 by awneil
Again, this is standard behaviour - whether for a phone or any other device.
But, again, the message will be held by the network until it can deliver it.
I suggest that you enable delivery notifications on the sending device - then you’ll know when the network has delivered the message.