Then the primary cells and mechanism could have been there a bit longer than Dave suggests based on the lifetime of a receiver continuously powered.
The receiver doesn't need to be continuously powered.
I'd have a system where it has two states - deep sleep and armed. In deep sleep, it powers up for a few milliseconds every few minutes. If it gets a signal, it goes into the armed state where it listens more frequently, or even all the time for the trigger signal. If it doesn't get triggered for half an hour or so, it could go back into the deep sleep mode. There would have been more than enough time to send such an arming signal in this case.
Let's say your receiver uses 20 mA and you listen for 10ms each second. On average, you are now only using 200 uA.
Alternatively, depending on the RF chip, it might be better to send out an "I'm listening now" signal and then power up the receiver just long enough to get a response. Some of these low power RF chips use less current to transmit than receive! If you don't know when your message is coming in, you have to power your receiver up long enough to receive two messages to ensure a message will be within your receive window - assuming a continuous stream if messages. So if you use less current to transmit and your messages are the same length, the poll method can actually use less power. It's certainly generating less useless RF on the part of the transmitter.
These sort of techniques are how a lot of low power wireless devices manage to run on coin cells. You spend most of your time in some deep sleep mode and run the radio at very low duty cycle.