Put RS485 microcontroller and transceiver to sleep and wake it up on incoming data
The DS36C279 is a RS485 transceiver with sleep mode, with a sleep mode current of 10uA. When you disabled both transmit and receive it enters sleep mode. The difficulty in using this part is that it cannot automatically wake an MCU from sleep, because when itself is in sleep it cannot receive data from the RS485 network.

You will need to design your system rather like a low power wireless system, where all nodes wake up at the same time to check if there is a transmission in progress that they need to receive. This synchronisation is often done at 1 to 10 second intervals, but you can chose the interval depending on the response time that you need. The real art of designing a good wireless system is maintaining precise synchronisation over a long period of time. But that's a different question.