Repairing an RFID antenna?
From the picture, the antenna looks like a PCB trace antenna. This means that it is simply a long, usually coiled, copper track  with a suitable impedance and radiation pattern.

Unless this board has been excessively and repeatedly flexed, it is unlikely that a trace has been broken. Alternatively, the board could have been scratched or gouged which causes the break - look for evidence of this.

The more obvious culprit would be the wire connection. Cables are always weak spots and a break inside the insulation is common. You can de-solder the ribbon cable and try a new one. The image doesn't make clear what the connector is, but its probably an IDC connector.

If that doesn't solve it, then you could have a problem with the transmitter. You could rule this out by flipping the wire and seeing if the other antenna now works. 

Lastly, you can replace the antenna PCB by redesigning the PCB and ordering new ones from a supplier such as OSHPark. You can try to copy the trace pattern by eye or use an RFID trace antenna calculator - check page 12 onwards.

Good luck.