If the system USED to work, nothing has happened that likely damaged the controller or wiring, and the rain sensor is wireless, the most likely point for the breakdown would be the communications between the sensor and the unit that connects to the controller. If so, then re-wiring the system won't solve the problem.
The simplest and cheapest way to attempt a quick fix would be try replacing all batteries (are there batteries in the base unit?).
After that, double checking the bypass setting as others have mentioned.
Finally, you might want to attempt to reprogram the transmitter address. The instructions say you shouldn't have to unless one of the parts was replaced. Here's some instructions I found with a Google search.
http://www.hrproducts.com.au/uploads/resources/Wireless%20Rain%20Clik%20June%2020,2005.pdf