RF Wakeup - Battling power consumption

The short answer is no, there is no such radio module. Note also that the two standby modes available cannot receive anything, they simply provide a faster start-up than is available from sleep mode.

To detect incoming packets you need to be in RX mode, so minimum 12.6mA. Clearly you can't stay in that mode all the time. You need to poll periodically. You could wake up once every two seconds for a few milliseconds. The transmitter would need to send a 2 second preamble before each packet. Even then the battery won't last very long.

Car keyless entry systems use two separate radios to overcome this. The first is an very low frequency (e.g. 145KHz) radio transmitter built into the car that works a bit like NFC/RFID contactless systems. When the user touches the door handle a burst is sent by the car that actually powers the receiver in the key, and thus the key doesn't need to continually power anything, or can at least do so at ultra low currents. Once this wake-up signal is received the car and key switch over to an ISM band radio, typically 433MHz, and do whatever security checks they need to do.

Replicating this over 3m is going to be a real stretch. Car systems are deliberately very short range, so people can't steal your car while you are filling it up.

The keyless entry system should send out a preamble/code at regular bursts, which the key wakes up and listens for. The key's RF module should be in power down mode for most of the time, along with the processor.

For example, the keyless entry systems send a 'ping' every 1ms, the key can wake up every 200ms and listen for the signal for 2ms, and if hears the ping, reply. You can play around with the periods to get the best battery life vs responsiveness that you like. With those numbers alone, the period the key is now on has been reduced to 1%. Have it wake every 1000ms instead and the key is on for 0.2%, but it takes at least 1 second for the key to work.

Obviously you'd need to use some form of low power counter on your micro, does it have a low power RTT or RTC? Or can you use the WDT to wake it up, check for radio contact and then go back to sleep?

CC1101 radio should consume 0.5 µA when in Wake on Radio (WOR) sleep mode.

See section 4.1 of the datasheet.

Thanks to Chris Stratton I realized that I missed the radio needs to periodically wake up, which makes CC2500 to consume depending on conditions 6.3 µA to 544.5 µA, see Current Consumption for a Polling Receiver.