Issue - I occasionally send texts that never make it to the recipient (issue with the mobile carrier or apple messaging, who knows..). But that person never knows they missed a message.
Solution - for each message conversation, have a counter that is appended at the end of each message (like a signature), that increments by 1 for each message I send. That way if person I'm texting to sees for example 38 at the end of a text, then next text its a 40, they can ask me to resend.

The counter could be setup to automatically reset to 1 after 99, or reset manually by the user if they would like to see a running total of texts sent to an individual.
And the counter is unique for each conversation.
For me, missing texts seem to usually be between my android device and someone using an Apple IOS device which uses their proprietary messaging service.