I'm facing a problem of message loss at the TE (Terminal End) when concurrent messages are sent. For Instance, when sending two messages at the same time, both are received by the modem, but one reaches the TE and the other goes to the Message Inbox.

In order to have the messages routed to the TE, you need to acknowledge receipt of each message before the next will download.
The acknowledgement is done with the +CNMA command.

Please see Receive Example 2 of our "how to_send and receive sms_edge" document at: