When I lived in Austin, I did many short connects in DFW and my bags never missed a connection.

Of course, it's always possible that the bags will miss, it does happen. The good news is that there are many (a dozen?) flights from DFW-SAT in a day, so they should make the next flight.

When I have had bags not make it at destinations, AA has delivered the bags to me. Even as far as Morgantown, WV when I flew into PIT (though that did take over 24 hours).